1

Problem

In a triangle XYZ, right-angled at Y, XY = 15 inches, and angle \$ X = 30^o\$. Find cos X.

2

Step

The given values are

XY = 15 inches, \$ X = 30^o\$

3

Clue

To find the cosine of angle X in the right triangle XYZ, you can use the definition of cosine, which is the ratio of the adjacent side to the hypotenuse.

4

Step

Find the length of side XZ (the hypotenuse) using trigonometric ratios in a right triangle. Using the sine function, we have:

\$ sin(X) = ("Opposite"​) /("Hypotenuse")\$

\$sin(30^o) = (XY)/(XZ)\$

\$1/2 = (15) / (XZ)\$

5

Step

Cross multiply:

\$XZ = (15)/(1/2)\$

\$XZ = 15 \times 2\$

XZ = 30 inches

6

Step

Now, calculate cosine X:

\$cos(X) = (XY) / (XZ)\$

\$cos(X) = 1/2\$

7

Solution

So, the cosine of angle X is \$1/2\$​.

8

Sumup

Please summarize Problem, Clue, Hint, Formula, Steps and Solution

Choices

9

Choice-A

Correct representation using the cosine formula

Correct \$1/2\$

10

Choice-B

The cosine function only outputs values between -1 and 1. Therefore, -2 is not a possible value for the cosine function so wrong

Wrong -2

11

Choice-C

This is incorrect. It states \$−1/2\$​, which is the cosine of 60 degrees, not 30 degrees

Wrong \$-1/2\$

12

Choice-D

The cosine of an angle cannot be greater than 1 or less than -1 because the cosine function’s range is between -1 and 1 so wrong

Wrong 2

13

Answer

Option

A

14

Sumup

Please summarize choices