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)

Question

Responses

31°
31°

39°
39°

53°
53°

37°
37°

Answer 1

To find the angle measure at vertex N in right triangle LMN, we can use the cosine function, which is defined as the ratio of the adjacent side to the hypotenuse.

Given:

• LM = 8 units (adjacent side to angle N)
• MN = 10 units (hypotenuse)

Using the cosine function:

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

To find the angle N, we take the inverse cosine (arccos) of 0.8:

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

Using a calculator:

\[ N \approx 36.87° \]

Rounding this to the nearest whole number, we find that angle N is approximately 37°.

Therefore, the correct answer is:

37°