Question

Right triangle LMN is drawn on paper. The right angle is located at vertex L with side length MN as the hypotenuse. The side length measurements are LM=8 units , MN=10 units , and NL=6 units . What is the approximate angle measure at vertex N ?(1 point)
Responses

37°
37°

39°
39°

53°
53°

31°

Answer 1

To find the angle measure at vertex \( N \) in triangle \( LMN \) where \( L \) is the right angle, we can use the sine, cosine, or tangent ratios. In this case, we'll use the cosine ratio since we have the lengths of both adjacent and hypotenuse sides.

First, we know:
- \( LM = 8 \) units (adjacent side to angle \( N \))
- \( MN = 10 \) units (hypotenuse)

Using the cosine formula:

\[
\cos(N) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{LM}{MN} = \frac{8}{10} = 0.8
\]

Now, we find \( N \) by taking the inverse cosine:

\[
N = \cos^{-1}(0.8)
\]

Calculating this gives:

\[
N \approx 36.87^\circ
\]

Rounding to the nearest degree would give us approximately \( 37^\circ \).

Thus, the angle measure at vertex \( N \) is approximately \( 37^\circ \). The correct response is:

**37°**