Question

question 7 of 10
fill in the blank. in the triangle below, y = ____. round your answer to two
decimal places.
triangle image: right triangle with right angle at bottom right, vertical leg 35, angle at top 52°, hypotenuse y, horizontal leg x, angle at bottom left z°
answer here

Explanation:

Step1: Identify the trigonometric ratio

The triangle is a right triangle. We know one angle (52°) and the adjacent side to this angle (35). We need to find the hypotenuse \( y \). The cosine function relates the adjacent side and the hypotenuse in a right triangle: \( \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \). Here, \( \theta = 52^\circ \), adjacent = 35, and hypotenuse = \( y \). So, \( \cos(52^\circ) = \frac{35}{y} \).

Step2: Solve for \( y \)

Rearrange the formula to solve for \( y \): \( y = \frac{35}{\cos(52^\circ)} \). Calculate \( \cos(52^\circ) \approx 0.6157 \) (using a calculator). Then, \( y = \frac{35}{0.6157} \approx 56.85 \).

Answer:

56.85