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Points A and B are on opposite sides of a lake. A point C is 91.791 meters from
a. The measure of ∠BAC ∠ B A C is 76.833°, and the measure of ∠ACB ∠ A C B is determined to be 31.683°. Find the distance between points A and
b.

Respuesta :

DeanR

We're given two angles and an included side and we want to solve for a side opposite one of the given angles. Using the typical triangle notation we have


b=AC=91.791 meters

A=76.833 degrees

C=31.683 degrees


and our task is to find c=AB.


To apply the Law of Sines we need B, which we get since the triangle angles add to 180 degrees:


B = 180 - A - C = 180 - 76.833 - 31.683 = 71.484 degrees


Now the Law of Sines says


[tex] \dfrac{b}{\sin B} = \dfrac{c}{\sin C}[/tex]


[tex]c = \dfrac{b \sin C}{\sin B}[/tex]


[tex] c = \dfrac{ 91.791 \sin 31.683^\circ }{\sin 71.484 ^\circ} = 50.842 [/tex]


Answer: 50.842 meters




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