Question

You need to find the distance across a river, so you make a triangle. BC is 661 feet, m∠B=103.2° and m∠C=14.4°. Find AB.

Answer 1

AB = 185.77 feet

Explanation:

From the figure attached, in ΔABC,

m∠B = 103.2°, m∠C = 14.4° and side BC = 661 feet

We have to find the measure of side AB.

Since ∠A + ∠B + ∠C = 180°

∠A + 103.2 + 14.4 = 180

∠A + 117.6 = 180

∠A = 180 - 117.6

= 62.4°

By applying sine rule in the given triangle ABC

`(AB)/(sinC)=(BC)/(sinA)`

`(AB)/(sin14.4)=(661)/(sin62.4)`

`(AB)/(0.249)=(661)/(0.886)`

AB =
`(0.249*661)/(0.886)`

= 185.77 feet

Therefore, AB = 185.77 feet will be the answer.