Math Problem Statement

Find x. Round your answer to the nearest tenth of a degree.

Solution

The image you uploaded contains a right triangle where you need to find the angle xx. To solve this, we can use trigonometric functions.

Given:

  • Hypotenuse = 21
  • Adjacent side = 18

We will use the cosine function, which relates the angle, adjacent side, and hypotenuse:

cos(x)=AdjacentHypotenuse\cos(x) = \frac{{\text{Adjacent}}}{{\text{Hypotenuse}}}

Substitute the given values:

cos(x)=1821=0.8571\cos(x) = \frac{{18}}{{21}} = 0.8571

Now, to find xx, take the inverse cosine:

x=cos1(0.8571)x = \cos^{-1}(0.8571)

Let me calculate that. math

Calculate the angle in degrees

cos_x = 18 / 21 x = math.degrees(math.acos(cos_x)) xThe value of xx is approximately 31.031.0^\circ, rounded to the nearest tenth.

Do you need any further details or clarifications on this problem?

Here are some related questions to consider:

  1. How do you calculate the other angles in a right triangle?
  2. What is the sine function, and how can it be used to find angles?
  3. How would you find the missing side in a right triangle if one angle and the hypotenuse are known?
  4. What is the tangent function, and how is it applied in right triangle problems?
  5. How do you solve for unknowns using the Pythagorean Theorem?

Tip: Always check if the given triangle is a right triangle before applying trigonometric ratios!

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Right Triangles
Cosine Function

Formulas

cos(x) = Adjacent / Hypotenuse
x = cos^{-1}(value)

Theorems

Trigonometric ratios in right triangles

Suitable Grade Level

Grades 8-10