If β = 83°, γ = 63° , c = 12.92 , find all unknown side lengths and angle measures. Round to the nearest hundredth for side lengths and angles, as needed.

Question

a ≈

b ≈

α = °

Answer 1

If β = 83°, γ = 63° , c = 12.92, find all unknown side lengths and angle measures. Round to the nearest hundredth for side lengths and angles, as needed. a ≈ , b ≈ , α = °

Detailed Solution:

Note: In order not to confuse students and myself, I completely avoid the Greek Alphabet β, γ, α. I keep it simple: If I call my vertex/angles: X, Y, Z, then my corresponding sides are x, y, z.

Simply: In this problem, here is what is given and missing:

Angles: A = ?? B = 83° C = 63° Sides: a = ?? b = ?? c = 12.92

Find Angle: A = 180° – (B + C) ==> A = 180° – (83° + 63°) ==> A = 180° – 146° ==> A = 34°

Use Law of Sines to find side a and side b: a/sin A = b/sin B = c/sin C

Find side a: a/sin A = c/sin C==> a/sin 34° = 12.92/sin 63°==> a = (12.92)(sin 34°)/(sin 63°) (Exact)==>

a = (12.92)(sin 34°)/(sin 63°) ==> a = 8.11 (Approximation)

Find side b: b/sin B = c/sin C==> b/sin 83° = 12.92/sin 63°==> b = (12.92)(sin 83°)/(sin 63°) (Exact)==>

b = (12.92)(sin 83°)/(sin 63°) ==> b = 14.39 (Approximation)

Therefore, here is the complete solution:

Angles: A = 34° B = 83° C = 63° Sides: a = 8.11 b = 14.39 c = 12.92

Answer 2

Draw and label a diagram!

α = 180° - 63° - 83°

Use Law of Sines to determine a and b