Unlock the Solution: Find the Value of X in the Triangle Illustrated on Khan Academy - Expert Answers!
Have you ever found yourself staring at a triangle and wondering how to find the value of x? Well, fear not! Khan Academy has got your back with step-by-step explanations and answers to that exact question. Let's dive in and solve this triangle together.
First, let's take a look at the triangle below and establish what we already know:
We can see that the triangle is a right triangle, meaning it contains a 90-degree angle. We also know that the two legs of the triangle are labeled as 3x and 2x + 5, while the hypotenuse is labeled as 17.
Now, to find the value of x, we can use the Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.
In other words, we can write the equation:
(3x)^2 + (2x + 5)^2 = 17^2
Expanding this equation and simplifying, we get:
9x^2 + 4x^2 + 20x + 25 = 289
Simplifying further, we get:
13x^2 + 20x - 264 = 0
Now we need to solve for x. We can do this by using the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
Where a, b, and c are coefficients of the quadratic equation ax^2 + bx + c = 0.
Plugging in the values we have:
x = (-20 ± sqrt(20^2 - 4(13)(-264))) / 2(13)
Simplifying, we get:
x = (-20 ± sqrt(21472)) / 26
Now we can use a calculator to find the two solutions. We get:
x ≈ -11.49 or x ≈ 5.89
However, we know that the length of a side cannot be negative, which means that x must be 5.89 in this case.
There you have it! The value of x in the given triangle is approximately 5.89. Khan Academy has once again provided a clear and concise explanation to a seemingly complicated problem. Remember to always check your work and never give up, no matter how challenging the problem may seem.
Now that you have successfully solved the triangle, it's time to put your skills to the test and try solving some more. Don't forget to practice regularly and seek help when needed.
If you enjoyed this article and want to learn more about math and its applications, be sure to check out Khan Academy's website for a wealth of educational resources and interactive lessons. Happy learning!
"Find The Value Of X In The Triangle Shown Below Khan Academy Answers" ~ bbaz
When it comes to mathematics, solving for X can be a daunting task, especially when it involves triangles. Fortunately, Khan Academy has provided a helpful triangle with all the necessary measurements for us to find the value of X. Let's dive into the problem and discover the steps needed to solve for X.
The Given Information
Before solving the problem, let's first familiarize ourselves with the given information. The triangle we are working with has a base of 6 cm and a height of 4 cm. Additionally, the hypotenuse measures 8 cm. We are tasked with finding the length of the second leg, represented by X.
Identifying the Type of Triangle
Based on the given information, we can determine that this is a right triangle. How do we know this? Well, the presence of a hypotenuse and a right angle (90 degrees) indicates that it is, in fact, a right triangle. This information will become important as we move forward with our calculations.
Using the Pythagorean Theorem
The Pythagorean Theorem is a well-known formula used to solve for the missing side lengths of a right triangle. The formula is a^2 + b^2 = c^2, where a and b are the two legs of the triangle, and c is the hypotenuse. In this case, we can plug in the known values and solve for X.
a^2 + b^2 = c^2
(4)^2 + (X)^2 = (8)^2
16 + X^2 = 64
Solving for X
Now that we have our equation set up, we can solve for X. To do this, we need to isolate X on one side of the equation. We can begin by subtracting 16 from both sides.
16 + X^2 - 16 = 64 - 16
X^2 = 48
Next, we can take the square root of both sides to find X.
X = √(48)
X = 6.93
Checking Our Answer
To ensure that we have solved for X correctly, we can use the Pythagorean Theorem again. This time, we can plug in our newly found value of X and verify that it fits with the original measurements.
a^2 + b^2 = c^2
(4)^2 + (6.93)^2 = (8)^2
16 + 48 = 64
As we can see, our answer checks out. Therefore, we can conclude that the value of X in the triangle shown is approximately 6.93 cm.
Conclusion
Solving for X in a right triangle may seem intimidating at first, but with the proper steps and formulas, it can be done with ease. It is crucial to understand the given information, identify the type of triangle, and use the right formula for the problem. By following these steps, we were able to solve for X in the triangle shown in Khan Academy.
Furthermore, understanding how to solve for X in a right triangle can be applied to real-world scenarios. For example, construction workers use right triangles when building structures to ensure that the angles are precise. Additionally, surveyors use them when measuring land areas. Therefore, it is essential to have a firm grasp of the concepts and formulas involved in solving for X in right triangles.
Find the Value of X in the Triangle Shown Below - A Comprehensive Comparison
Introduction
Geometry is an intriguing subject that has always been an integral part of mathematics. It involves studying shapes, sizes, positions, angles, and dimensions of objects, among other things. One such concept that we study in geometry is the triangle. Triangles can be formed in several ways and have different properties, but they all share one thing in common - their angles add up to 180 degrees. In this blog post, we'll focus on finding the value of x in the triangle shown below, using Khan Academy answers as a reference.Understanding the Triangle
The triangle shown below has an angle labeled as 70°, another angle as x, and the third angle as 60°. Our task is to find the value of x.
Method 1 - Using Sum of Angles
One of the fundamental concepts of geometry is that the sum of the angles in any triangle is 180°. Therefore, to find the value of x in this triangle, we can first add up the other two angles (70° + 60°) and then subtract the result from 180°.| Method 1 | Formula Used | Steps | Result |
|---|---|---|---|
| Sum of Angles | (Sum of Known Angles) = 180° - x | (70° + 60°) = 180° - x | x = 50° |
Method 2 - Using Exterior Angles Theorem
Another way to find the value of x in this triangle is to use the Exterior Angles Theorem. According to this theorem, the measure of an exterior angle of a triangle is equal to the sum of the measures of the two opposite interior angles. In other words, if we draw a line parallel to one side of the triangle and extend it, we will get an exterior angle that is equal to the sum of the two opposite interior angles.
| Method 2 | Formula Used | Steps | Result |
|---|---|---|---|
| Exterior Angles Theorem | x = 70° + 60° | x = 130° | x = 50° |
Comparison of Methods
Both methods discussed above yielded the same result, i.e., x = 50°. However, they differ in their approaches. The first method (Sum of Angles) is based on the fact that the sum of the angles in a triangle is always 180°, whereas the second method (Exterior Angles Theorem) uses the fact that the exterior angle of a triangle is equal to the sum of the two interior opposite angles. The first method is more general and can be applied to any triangle, whereas the second method is specific to finding an angle between two sides of a triangle. The first method can be used when one or two angles are known, but the second method requires a parallel line to be drawn, which may not always be feasible.Conclusion
In conclusion, geometry is an essential branch of mathematics that involves studying shapes, sizes, positions, angles, and dimensions. We discussed how to find the value of x in a triangle using two different methods - Sum of Angles and Exterior Angles Theorem. Both methods led us to the same result, i.e., x = 50°. However, they differ in their approaches and applications. It is crucial to understand the underlying concepts behind each method and choose the appropriate one based on the given problem.Find the Value of X in the Triangle Shown Below Khan Academy Answers
Introduction
In geometry, triangles are one of the basic shapes studied. They are important in computing the perimeter and area of figures. In a triangle, the sum of the angles is 180 degrees. Sometimes, we need to find the value of an angle or a side length in a triangle. This article will show you how to find the value of x in a triangle, as given in Khan Academy.Given Information
The triangle shown has two equal angles and one unknown angle. The side lengths are x + 5, x + 3, and x.Solution
To find the value of x in this triangle, we need to use the fact that the sum of the angles in a triangle is 180°. Let's call the unknown angle A, and the other two angles B and C. Because two of the angles are equal, we know that A + B + C = 180°A + 2B = 180°Substituting x + 5 for side AB and x + 3 for side AC gives us the following equation using the Law of Cosines:cos(B) = (x + 3)^2 + x^2 - (x + 5)^2 / 2(x + 3)(x)cos(B) = (2x + 4) / 2(x + 3)(x)cos(B) = (x + 2) / (x^2 + 3x)We can substitute this into our earlier equation to get A + 2B = 180°A + 2cos^-1 [(x + 2) / (x^2 + 3x)] = 180°We can simplify this equation into A = 180° - 2cos^-1 [(x + 2) / (x^2 + 3x)]Now let's substitute A, B, and C back into our first equation. We get thatA + B + C = 180°180° - 2cos^-1 [(x + 2) / (x^2 + 3x)] + 2cos^-1 [(x + 2) / (x^2 + 3x)] + cos^-1 [(x + 3) / x] = 180°Simplifying this gives us cos^-1 [(x + 3) / x] = cos^-1 [(x^2 + 5x + 8) / x(x + 3)]We can convert this trigonometric equation to a polynomial equation as x(x + 3) * sqrt[x(x + 6)] = x^2 + 5x + 8Simplifying this polynomial equation gives us x^4 + 3x^3 - 11x^2 - 24x - 48 = 0We can factorize this polynomial equation as (x + 3)(x^3 - 8x^2 - 35x - 16) = 0Therefore, the value of x that satisfies the given conditions in the triangle is either -3 or approximately 4.15. However, because negative values do not make sense for the sides of a triangle, we choose the root, x ≈ 4.15.Conclusion
In this article, we learned how to find the value of x in a triangle given the side lengths and angle measures. We used the fact that the sum of the angles in a triangle is 180 degrees, the Law of Cosines and trigonometric equations. By following the steps, we were able to find the value of x ≈ 4.15, which satisfies the given conditions in the triangle.Find The Value Of X In The Triangle Shown Below Khan Academy Answers
Welcome to this tutorial where we will learn how to find the value of x in a triangle. Geometry can be a challenging subject, but with our step-by-step guide, you will have a better understanding of how to solve geometric problems, particularly those involving triangles.
Triangles are essential figures in geometry, and they come in different shapes and sizes. They are composed of three sides, three angles, and three vertices. To solve problems involving triangles, we need to understand some of their properties, such as the sum of angles, congruence rules, and area formulas.
In this tutorial, we will focus on finding the value of x in a triangle, like the one shown below:
To solve the problem, we need to use the properties of triangles that involve the sum of angles and congruent triangles. Let us break down the triangle into smaller parts to make it easier to analyze.
First, we notice that there is a right triangle with an angle measurement of 90 degrees. Therefore, we can use the Pythagorean theorem to find the length of the hypotenuse BC, which is the longest side of the triangle.
Let us label the length of AB as a and the length of AC as b. Using the Pythagorean theorem, we get:
a² + b² = c²
Where c is the length of BC. Substituting the given values, we get:
5² + 12² = c²
169 = c²
c = 13
Now we know that the length of BC is 13 units. Let us label angle BAC as y. From the given information, we know that angle ABC has a measurement of 60 degrees.
Using the property that the sum of angles in a triangle is 180 degrees, we can find angle BAC as follows:
60 + 90 + y = 180
y = 30
We now know that angle BAC has a measurement of 30 degrees. Let us label angle BCA as z. We can use the property that the sum of angles in a triangle is 180 degrees to find angle BCA:
z + 90 + 30 = 180
z = 60
We have found that angle BCA has a measurement of 60 degrees. Now we can use the sine, cosine, and tangent ratios to find the value of x. Let us label angle ABC as t.
We can use the sine ratio in triangle ABC:
sin t = opposite / hypotenuse = a / c
sin 60 = x / 13
x = 13 * sin 60
x ≈ 11.3
Therefore, the value of x is approximately 11.3 units.
Now that you have learned how to find the value of x in a triangle, you can apply this knowledge to solve more complex problems involving triangles. Remember to use the properties of triangles, such as the sum of angles and congruence rules, to your advantage when solving geometric problems.
Thank you for reading this tutorial about finding the value of x in a triangle. We hope it was informative and helpful in improving your understanding of geometry. If you have any questions or comments, please feel free to leave them below. Good luck with your future studies!
People Also Ask About Find The Value Of X In The Triangle Shown Below Khan Academy Answers
What is the problem about?
The problem is about finding the value of x in a triangle that is given with some angles and measurements.
What is given in the problem?
- Angle A = 50 degrees
- Angle B = x degrees
- Angle C = 80 degrees
- Side b = 8 cm
- Side c = 7 cm
How can we solve the problem?
We can solve the problem using the law of cosines formula which is:
c^2 = a^2 + b^2 - 2ab(cos(C))
where c is the side opposite to angle C, a is the side opposite to angle A, and b is the side opposite to angle B.
Using this formula, we can find the value of side a which is:
a^2 = c^2 + b^2 - 2bc(cos(A))
a^2 = 7^2 + 8^2 - 2(7)(8)(cos(50))
a^2 = 77.58
a = 8.8 (rounded to one decimal place)
Now, we can use the law of sines formula to find the value of x which is:
(sin(B)) / b = (sin(A)) / a
sin(B) = (b/a)(sin(A))
sin(B) = (8/8.8)(sin(50))
sin(B) = 0.68
B = 43.70 degrees (rounded to two decimal places)
What is the final value of x?
The final value of x is 180 - A - B = 86.3 degrees (rounded to one decimal place).
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