law of sines trig

Question

Find all the missing elements

A=50° B=?

C=35° a=?

b=13 b=?

Answer 1

Use the fact that the angles in a triangle sum to 180 degrees to find the missing angle.

Then use the law of sines to find the missing sides. sinA/a = sinB/b = sinC/c

Answer 2

Hi Grace G.,

Law of sines: a/sin(A) = b/sin(B) = c/sin(C). For triangle abc we know angles ∠A = 50⁰ and ∠C = 35⁰. And the angles of any triangle add to 180⁰.

Therefore ∠B = 180⁰ - (∠A + ∠C) = 180⁰ - (50⁰ + 35⁰) = 180⁰ - 85⁰ = 95⁰.

Using a/sin(A) = b/sin(B):

a/sin(50⁰) = 13/sin(95⁰),

a = 13*sin(50⁰)/sin(95⁰) = 10

Using c/sin(C) = b/sin(B):

c/sin(35⁰) = 13/sin(95⁰),

c = 13*sin(35⁰)/sin(95⁰) = 7.5

I hope this helps, Joe.