Question

Use the Law of Cosines to find the measure of angle M to the nearest degree.

Answer 1

LK^2=KM^2+LM^2-2*KM*LM*cos M
225=100+400-400*cos M
400cosM=275
cosM=275/400=0.68
M=47

Answer 2

angle M = 47°

Explanation:

By the law of cosine.

KL² = ML² + MK² - 2 (ML) (MK) cosM

Here KL = 15 ft.

MK = 10 ft.

ML = 20 ft.

Now we place the values in the formula

(15)² = (20)² + (10)² - 2(20)(10) cosM

225 = 400 + 100 - 400 cosM

225 - 500 - 400 cosM

225 - 500 = -400 cosM

-400 cosM = -275

cosM =
`(275)/(400)` = 0.6875

M = cos⁻¹ (0.6875)

= 46.57° ≈ 47°

Therefore, angle M = 47°