Solve the triangle. A = 51°, b = 11, c = 7

Answer 1

The triangle measurements are A = 51°, b = 11 , c = 7

Solve the triangle by using SAS rule.

To solve the traingle we need to find remaining side a and angles B and C.

Use law of cosines

a² = b² + c² - 2bc cosA

a² = (11)² + (7)² - 2(11)(7) cos(51)

a² = 121 + 49 - 154 cos(51)

a² = 170 - 154(0.629)

a² = 170 - 96.866

a² = 73.134

a = 8.55

Now use law of sines sinA/a = sinB/b

sin(51)/ 8.55 = sin(B)/11

sin(B) = 11[sin(51)/ 8.55]

sin(B) = 11[0.777/8.55]

B = sin^-1(0.999)

B = 87.43°

Sum of angles in triangle = 180°

A + B + C = 180

C = 180 - (A + B)

C = 180 - (51 + 87.43)

C = 180 - 138.43

C = 41.57°

Comments

THIS ANSWER IS WRONG