Question

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

A. 43°
B. 48°
C. 31°
D. 84°

Answer 1

Answer: option B. 48°

Step-by-step 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°

Answer 2

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)= (k^(2) + l^(2)- j^(2))/(2(k)(l))`

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


`cos(J)= ( 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