Question

find the value of ( x ). round your answer to two decimal places. enter deg after any degree value.

image of a right triangle def with right angle at f, angle at d is 49 degrees, side df is 36, and hypotenuse de is ( x ).

Explanation:

Step1: Identify the trigonometric ratio

In right triangle \( DEF \), \( \angle F = 90^\circ \), \( \angle D = 49^\circ \), and the adjacent side to \( \angle D \) is \( DF = 36 \), and the hypotenuse is \( DE = x \). We use the cosine function, which is \( \cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}} \). So, \( \cos(49^\circ)=\frac{DF}{DE}=\frac{36}{x} \).

Step2: Solve for \( x \)

Rearrange the formula to solve for \( x \): \( x = \frac{36}{\cos(49^\circ)} \). Calculate \( \cos(49^\circ) \approx 0.6561 \). Then \( x=\frac{36}{0.6561}\approx 54.87 \).

Answer:

\( 54.87 \)