Right triangle

Question

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)
0 37°
031°
• 39°
• 53°

Answer 1

To find the approximate angle measure at vertex N in the right triangle LMN, we can use the sine, cosine, or tangent functions. Since we are given the lengths of all sides, we can use the cosine function as follows:

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

Using the values from the triangle:

• \(LM = 8\) units (adjacent side)
• \(MN = 10\) units (hypotenuse)

Thus,

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

Now, we can find the angle N using the inverse cosine function:

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

Calculating that gives us:

\[ N \approx 36.87° \]

Rounding to the nearest degree, this is approximately 37°.

So, the approximate angle measure at vertex N is 37°.