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. A. 299 ft B. 168 ft C. 185 ft D. 188 ft

Answer 1

check the picture below.

recall the angle at A is 180° - 103.2° - 14.4°.

Answer 2

The correct option is: C. 185 ft

Explanation:

In
`\triangle ABC`,
`m\angle B=103.2`° and
`m\angle C=14.4`°

As the sum of three angles in any triangle is always 180°, so
`m\angle A= 180-(103.2+14.4)=180-117.6=62.4`°

Given that,
`BC= 661\ ft`

Using the Sine rule, we will get......

`(AB)/(Sin(C))=(BC)/(Sin(A))\\ \\ (AB)/(Sin(14.4))=(661)/(Sin(62.4))\\ \\ AB=(661*Sin(14.4))/(Sin(62.4))=185.492...\approx 185\ ft`