Question

You need to find the distance across a river, so you make a triangle. BC is 943 feet, m∠B=102.9° and m∠C=18.6°. Find AB.

Answer 1

The length of AB is 352.8 feet

Explanation:

* Lets revise some facts to solve the problem

- The sine rule:
`(sinA)/(BC)=(sinB)/(AC)=(sinC)/(AB)`

- The sum of the measures of the interior angles of a triangle is 180°

* Lets solve the problem

- In Δ ABC

∵ m∠ B = 102.9°

∵ m∠ C = 18.6°

∵ m ∠A + m∠ B + m∠ C = 180° ⇒ interior angles of a Δ

∴ m ∠A + 102.9 + 18.6 = 180

∴ m ∠A + 121.5 = 180 ⇒ subtract 121.5 from both sides

∴ m∠A = 58.5°

* Lets use the sine rule to find AB

∵ BC = 943

∵ m∠A = 58.5°

∵ m∠ C = 18.6°

∴
`(sin(58.5))/(943)=(sin(18.6))/(AB)`

- By using cross multiplication

∴ AB × sin(58.5) = 943 × sin(18.6)

- Divide both sides by sin(58.5)

∴ AB = [943 × sin(18.6)] ÷ sin(58.5) = 352.76 ≅ 352.8

* The length of AB is 352.8 feet

Answer 2

352.8 feet

Explanation:

The given triangle is drawn in the image attached with. Note that the image is not drawn to scale.

We can find the length of AB using the law of sines. According to which:

`(a)/(sin(A))=(b)/(sin(B))=(c)/(sin(C))`

Since sum of angles in a triangle is 180, we can write:

A + B + C = 180

A + 102.9 + 18.6 = 180

A = 58.5

Using the values, in the law of sines, we get:

`(943)/(sin(58.5)) = (c)/(sin(18.6))\\\\ c = (943 * sin(18.6))/(sin(58.5))\\\\ c = 352.8`

Thus, the measure of side AB would be 352.8 feet