Question

Law of cosines: a2 = b2 + c2 – 2bccos(A) What is the measure of N to the nearest whole degree? 35° 45° 55° 65° The triangle sides are 7 4 5.74

Answer 1

C. 55

Explanation:

5.74^2 = 4^2 + 7^2 -2(4)(7)cos(N)

32.9 = 65 -56cos(N)

-32.1 = -56cos(N)

-32.1/-56 = cos(N)

cos^-1 = 55.0253

m angle N = 55

Answer 2

option C

N ≈ 55°

Explanation:

Given in the question a right angle triangle.

To calculate the angle N, we will use following formula

a² = b² + c² -2bcCos(A)

here,

a = 5.74

b = 4

c = 7

A = N°

Plug values in the formula

5.74² = 4² + 7² -2(4)(7)COS(N)

32.95 = 16 + 49 - 56COS(N)

32.95 = 65 - 56COS(N)

32.95 - 65 = - 56COS(N)

-32.05 = - 56COS(N)

minus will cancel out

32.05 = 56COS(N)

COS(N) = 32.05/56

COS(N) = 0.57

N =
`cos^(-1)`(0.57)

N = 55.08°

N ≈ 55°