Question

Use the inverse of the tangent ratio to find the approximate measure of the missing angle. Round your answer to the nearest whole degree. ( It's an ABC triangle. We do have a right angle. The two sides we know are, 2cm and 5cm. We don't know the last side.)

Answer 1

To determine the missing angle in a right triangle using the inverse tangent ratio, we need to identify the sides relevant to the angle we're calculating.

Let's denote the triangle as follows:
- Let angle \( C \) be the right angle.
- Let angle \( A \) be the angle opposite to the side measuring 2 cm.
- Let angle \( B \) be the angle opposite to the side measuring 5 cm.

To find angle \( A \) using the inverse tangent ratio:

1. Identify the sides relative to angle \( A \):
- The side opposite angle \( A \) is 2 cm.
- The side adjacent to angle \( A \) is 5 cm.

2. Use the tangent ratio:
\[
\tan(A) = \frac{\text{opposite}}{\text{adjacent}} = \frac{2}{5}
\]

3. Apply the inverse tangent function to find angle \( A \):
\[
A = \tan^{-1}\left(\frac{2}{5}\right)
\]

4. Calculate using a calculator:
\[
A \approx \tan^{-1}(0.4) \approx 21.8 \text{ degrees}
\]

5. Round to the nearest whole degree:
\[
A \approx 22 \text{ degrees}
\]

Thus, the approximate measure of the missing angle \( A \) is **22 degrees**.