Question

In triangle ABC, b = 600, ∠B = 11°, and ∠C = 75°. Find a.

115
1,185
3,037
3,137

Answer 1

a = 3,137

Explanation:

We have to use the sin rule to solve. THis gives ratios of side and opposite side's angle's sin.

Sin rule is:

`(a)/(SinA)=(b)/(SinB)=(c)/(SinC)`

First, we know there are 180 degrees in 3 angles of a triangle, so lets find ∠A:

∠A + ∠B + ∠C = 180

∠A + 11 + 75 = 180

∠A + 86 = 180

∠A = 180 - 86

∠A = 94

Now since we know the angle B and side b pair, we can relate with a and write the sin rule as:

`(a)/(SinA)=(b)/(SinB)\\(a)/(Sin94)=(600)/(Sin11)`

Now we cross multiply and solve for side a:

`(a)/(Sin94)=(600)/(Sin11)\\aSin11=600Sin94\\a=(600Sin94)/(Sin11)\\a=3137`

So last answer choice is right, a = 3137