Right triangle LMN

Question

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

31°
31°

53°
53°

39°
39°

37°

Answer 1

To find the approximate angle measure at vertex N in triangle LMN, we can use the cosine rule or the sine rule. In this case, we can use the sine rule which relates the angles and sides of a triangle.

Using the sine function, we'll find \(\sin(N)\):

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

Now, we can find the angle \(N\) using the arcsin function:

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

Calculating this gives:

\[ N \approx 53° \]

Thus, the approximate angle measure at vertex N is 53°.