Questions: Find h as indicated in the figure. h = □ (Round to the nearest integer as needed.) 27.2° 30.4° 315 h

Solution Steps

We are given the angle \(27.7^\circ\) and the adjacent side with length 315. We need to find the opposite side, denoted by 'h'. The trigonometric ratio relating the opposite side and the adjacent side is the tangent function:

\(\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}\)

In our case, \(\theta = 27.7^\circ\), the adjacent side is 315, and the opposite side is h. Therefore, we have:

\(\tan(27.7^\circ) = \frac{h}{315}\)

To solve for h, we multiply both sides of the equation by 315:

\(h = 315 \cdot \tan(27.7^\circ)\)

Using a calculator, we find:

\(h \approx 315 \cdot 0.5242 \approx 165.07\)

Rounding to the nearest integer, we get:

\(h \approx 165\)

Final Answer