Question

Use the inverse of cosine to solve for the missing angle, rounded to the nearest whole degree.
Imagine a right triangle. The top slanted line is labelled 5, the side line is 3, and the bottom line is 4.

Answer 1

To find the missing angle in the right triangle, we can use the cosine function. In a right triangle, the cosine of an angle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse.

In this triangle:
- The hypotenuse (the slanted side) is 5.
- The adjacent side (the side next to the angle we want to find) is 4.

We can use the inverse cosine function (cosine inverse or \(\cos^{-1}\)) to find the angle. Let's denote the angle we want to find as \( \theta \).

The cosine of \( \theta \) is given by:
\[
\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{4}{5}
\]

Now calculating the angle:
\[
\theta = \cos^{-1}\left(\frac{4}{5}\right)
\]

Now we can compute this using a calculator:
\[
\theta \approx \cos^{-1}(0.8)
\]

Calculating it:
\[
\theta \approx 36.87^\circ
\]

Rounding to the nearest whole degree:
\[
\theta \approx 37^\circ
\]

Thus, the missing angle rounded to the nearest whole degree is \( \boxed{37} \).