Question

side of triangle: 2 cm
side of triangle: 5 cm

Use the inverse of tangent ratio to find the approximate measure of the missing angle. Round your answer to the nearest whole degree.

a. 21
b. 12
c. 44
d. 22

Answer 1

To find the missing angle in a triangle using the inverse tangent ratio (also known as arctan), we need to know the relationship between the sides.

It seems you have two sides of a right triangle: one side measuring 2 cm and the other side measuring 5 cm.

Assuming:
- 2 cm is the opposite side of the angle we want to find.
- 5 cm is the adjacent side.

We can use the tangent ratio:

\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{2}{5}
\]

To find the angle \(\theta\), we take the inverse tangent:

\[
\theta = \arctan\left(\frac{2}{5}\right)
\]

Calculating this gives:

\[
\theta \approx \arctan(0.4) \approx 21.8 \text{ degrees}
\]

Rounding this to the nearest whole degree gives us approximately 22 degrees.

Thus, the answer is:
**d. 22**