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

Answer:

The correct option is:  C.  185 ft

Step-by-step 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......

$\frac{AB}{Sin(C)}=\frac{BC}{Sin(A)}\\ \\ \frac{AB}{Sin(14.4)}=\frac{661}{Sin(62.4)}\\ \\ AB=\frac{661*Sin(14.4)}{Sin(62.4)}=185.492...\approx 185\ ft$