Question

find the length x to the nearest whole number.
(do not round until the final answer. then round to the nearest whole number.)

Explanation:

Step1: Find the adjacent side for 69°

Let the adjacent side for 69° be \( a \). Using \( \tan(69^\circ)=\frac{400}{a} \), so \( a = \frac{400}{\tan(69^\circ)} \).
\( \tan(69^\circ)\approx2.605 \), so \( a\approx\frac{400}{2.605}\approx153.55 \).

Step2: Find the adjacent side for 36°

Let the adjacent side for 36° be \( b \). Using \( \tan(36^\circ)=\frac{400}{b} \), so \( b = \frac{400}{\tan(36^\circ)} \).
\( \tan(36^\circ)\approx0.7265 \), so \( b\approx\frac{400}{0.7265}\approx550.59 \).

Step3: Calculate x

\( x = b - a \approx550.59 - 153.55 = 397.04 \approx 397 \).

Answer:

\( 397 \)