Question

Use the Law of Cosines to find the missing angle. In triangle JKL, j=3in., k=4in., and l=2.89., find mJ

Answer 1

Using the law of cosine for Triangle KJL, we can write:

$j^{2} = k^{2} + l^{2}-2(k)(l)cos(J) \\ \\ 2(k)(l)cos(J)=k^{2} + l^{2}- j^{2} \\ \\ cos(J)= \frac{k^{2} + l^{2}- j^{2}}{2(k)(l)}$

Using the values of k,j and l, we can write:

$cos(J)= \frac{ 4^{2} + (2.89)^{2} - 3^{2} }{2(4)(2.89)} \\ \\ cos(J)= 0.664 \\ \\ J= cos^{-1}(0.664) \\ \\ J=48.39$

Rounding to nearest integer, the measure of angle J will be 48 degrees.
So option B gives the correct answer

Answer 2

Answer: option B. 48°

Explanation:


1) Data:
side j: 3 in

side k: 4in
side l: 2.89 in
angle J: ?

2) Law of cosines

j² = k² + l² - 2kl cos(J)

⇒ 3² = 4² + (2.89)² - 2(4)(2.89)cos(J)

⇒ cos(J) = [16 + 8.3521 - 9] / (23.12)

⇒cos(J) = 0.66402
⇒ J = arc cosine (0.66402) ≈ 48.39°