Question

what is the measure of ∠n to the nearest whole degree?
35°
45°
55°
65°
law of cosines: a² = b² + c² - 2bc cos(a)

Explanation:

Step1: Identify the sides for cosine formula

In right - triangle MLN, if we want to find $\angle N$, we can use the cosine function $\cos(N)=\frac{LN}{MN}$. Here, $LN = 4$ and $MN=7$.

Step2: Calculate the cosine value

$\cos(N)=\frac{4}{7}\approx0.5714$.

Step3: Find the angle

$N=\cos^{- 1}(0.5714)$. Using a calculator, $N\approx55^{\circ}$.

Answer:

$55^{\circ}$