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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

You need to find the distance across a river so you make a triangle BC is 661 feet mB1032 and mC144 Find AB A 299 ft B 168 ft C 185 ft D 188 ft class=

Respuesta :

check the picture below.


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

Ver imagen jdoe0001

Answer:

The correct option is:  C.  185 ft

Step-by-step explanation:

In [tex]\triangle ABC[/tex], [tex]m\angle B=103.2[/tex]° and [tex]m\angle C=14.4[/tex]°

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

Given that, [tex]BC= 661\ ft[/tex]

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

[tex]\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[/tex]

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