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andrezito [222]
3 years ago
9

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

Mathematics
2 answers:
Gnoma [55]3 years ago
8 0

check the picture below.


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

Ivahew [28]3 years ago
4 0

Answer:

<em>The correct option is:  C.  185 ft</em>

Step-by-step explanation:

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

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

Given that, BC= 661\ ft

<u>Using the Sine rule</u>, 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

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