Question

Solve for x. Round to the nearest tenth, if necessary.
Hypotenuse = 83
Angle = 41
Adjacent = ?

Answer 1

To find the length of the adjacent side in a right triangle given the hypotenuse and an angle, you can use the cosine function. The cosine of an angle in a right triangle is defined as the ratio of the length of the adjacent side to the hypotenuse.

The formula is:

\[
\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}
\]

In this case, you are given:

- Hypotenuse (\(h\)) = 83
- Angle (\(\theta\)) = 41 degrees

You want to find the length of the adjacent side (\(a\)). Rearranging the formula gives:

\[
a = h \cdot \cos(\theta)
\]

Now, substituting the values into the equation:

\[
a = 83 \cdot \cos(41^\circ)
\]

Using a calculator to find \(\cos(41^\circ)\):

\(\cos(41^\circ) \approx 0.7547\)

Now calculate \(a\):

\[
a = 83 \cdot 0.7547 \approx 62.7461
\]

Rounding to the nearest tenth:

\[
a \approx 62.7
\]

So, the length of the adjacent side is approximately **62.7**.