Question
Look at the triangle:
A right angle triangle is shown with hypotenuse equal to 17 centimeters. An acute angle of the triangle is labeled as x degrees. The side adjacent to the acute angle has length 15 centimeters, and the side opposite to the acute angle has length 8 centimeters.
What is the value of cos x°?
8 ÷ 17
17 ÷ 8
15 ÷ 17
8 ÷ 15
Answers
GPT-4o mini
To find the value of \( \cos x^\circ \) in the right triangle you've described, we can use the definition of the cosine function in relation to a right triangle.
The cosine of an angle in a right triangle is defined as the ratio of the length of the adjacent side to the hypotenuse. In this case, the adjacent side has a length of 15 cm, and the hypotenuse has a length of 17 cm.
Thus, we have:
\[
\cos x^\circ = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{15}{17}
\]
So, the value of \( \cos x^\circ \) is \( \frac{15}{17} \). Therefore, the correct option is:
- **15 ÷ 17**.
The cosine of an angle in a right triangle is defined as the ratio of the length of the adjacent side to the hypotenuse. In this case, the adjacent side has a length of 15 cm, and the hypotenuse has a length of 17 cm.
Thus, we have:
\[
\cos x^\circ = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{15}{17}
\]
So, the value of \( \cos x^\circ \) is \( \frac{15}{17} \). Therefore, the correct option is:
- **15 ÷ 17**.