Question

You are given a triangle that has sides 5 7 ad 10 how large is the smallest angle of the triangle

Answer 1

Explanation:

Comment

This uses the cosine Law for line length.

Formula

a^2 = b^2 + c^2 - 2*b*c*sin(A)

Givens

a = 5

b = 7

c = 10

Solution

5^2 = 7^2 + 10^2 - 2*7*10*cos(A)

25 = 49 + 100 - 140*cos(A) Combine the right side

25 = 149 - 140 * cos(A) Subtract 149 from both sides

25 - 149 = - 140*cos(A)

-124 = -140 * cos(A) Divide both sides by -140

-124/-140 = cos(A)

Cos(A) = 0.8857 Take the inverse Cos of both sides

A = cos-1(0.8857)

Answer

A = 27.66 degrees