What is angle E to the nearest degree in the triangle EFG where FG is 89 inches EG is 77 inches and angle G is 132 degrees?

Answer 1

This can be solved using the cosine rule to find the length of side EF, and the sine rule to find angle E

The cosine rule is:

a² = b² + c² - 2bc cos A

we have:

A = G = 132°

a = EF

b = EG = 77 inches

c = FG = 89 inches

(the assignment of b and c doesn't matter as they are the two sides of the angle A and are interchangeable for the cosine rule), giving:

EF² = 77² + 89² - 2×77×89×cos 132°

→ EF = √(77² + 89² - 2×77×89×cos 132°)

The sine rule is: (sin A)/a = (sin B)/b = (sin C)/C

we have:

A = G = 132°

a = EF = √(77² + 89² - 2×77×89×cos 132°) inches (found above)

C = E

c = FG = 89 inches

→ (sin 132°)/√(77² + 89² - 2×77×89×cos 132°) in = (sin E)/89 in

→ sin E = (89 sin 132°)/√(77² + 89² - 2×77×89×cos 132°)

→ E = arc sin((89 sin 132°)/√(77² + 89² - 2×77×89×cos 132°))

→ E ≈ 25.8°

→ E ≈ 26° to the nearest degree