Question

select the correct answer from the drop - down menu. larry is building a fence. each side of the real measures 14 feet. the measure of the angle between the two sides of the real is approximately

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines formula for finding an angle $\theta$ in a triangle with sides $a$, $b$, $c$ is $c^{2}=a^{2}+b^{2}-2ab\cos\theta$. Let $a = 14$, $b = 14$, and $c = 20$. Then $20^{2}=14^{2}+14^{2}-2\times14\times14\times\cos x$.

Step2: Simplify the equation

$400 = 196+196 - 392\cos x$. Combine like - terms: $400=392 - 392\cos x$. Rearrange to get $392\cos x=392 - 400=-8$. So, $\cos x=\frac{-8}{392}=-\frac{2}{98}=-\frac{1}{49}$.

Step3: Find the angle

$x=\cos^{-1}(-\frac{1}{49})\approx 91.16^{\circ}\approx92^{\circ}$ (rounded to the nearest degree).

Answer:

$92$