Question

In a right triangle with legs 5 cm and 12 cm long, find the measure of the smallest angle.
(1 point)
Responses

22.6°
22.6°

24.6°
24.6°

65.4°
65.4°

67.4°

Answer 1

To find the measure of the smallest angle in a right triangle with legs of lengths 5 cm and 12 cm, we can use the tangent function. In this triangle, we can label the legs as follows:

- Let \( a = 5 \) cm (one leg)
- Let \( b = 12 \) cm (the other leg)

The smallest angle will be opposite the shortest leg (5 cm). We can use the tangent function, which is defined as:

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

In this case, the smallest angle \( \theta \) is opposite the leg of length 5 cm, and the adjacent leg is the length of 12 cm:

\[
\tan(\theta) = \frac{5}{12}
\]

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

\[
\theta = \tan^{-1} \left( \frac{5}{12} \right)
\]

Now we can calculate this using a calculator:

\[
\theta \approx \tan^{-1}(0.4167) \approx 22.6°
\]

Therefore, the measure of the smallest angle is approximately \( 22.6° \).

So, the correct response is:

**22.6°**