Question

Question
A portion of the roof of a modern house resembles a right triangle. The roof slopes away from the house, creating a slope of 724
. Using the inverse of sine, what is the approximate angle formed at the top of the roof? Round your answer to the nearest whole degree.(1 point)
°

Answer 1

To determine the angle formed at the top of the roof using the slope of \(724\), we need to understand that the slope is essentially a ratio of the rise (height) to the run (horizontal distance). In this case, let's assume the rise is \(724\) units, and the run is \(1\) unit.

The sine function relates an angle in a right triangle to the ratio of the opposite side (rise) to the hypotenuse. Thus, we need to define the angle \( \theta \) such that:

\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}
\]

However, we actually need to use the tangent function because the slope is typically defined in terms of rise over run:
\[
\tan(\theta) = \frac{\text{rise}}{\text{run}} = \frac{724}{1} = 724
\]

Now, we need to find the angle \( \theta \):
\[
\theta = \tan^{-1}(724)
\]

Using a calculator to find this inverse tangent:
\[
\theta \approx \tan^{-1}(724) \approx 89.2 \text{ degrees}
\]

Rounding to the nearest whole degree, we find:
\[
\theta \approx 89 \text{ degrees}
\]

So the approximate angle formed at the top of the roof is \( \boxed{89} \) degrees.