Question

Please use the law of sines to show me how to solve the triangle please. Thank you .

Answer 1

sin(A) / a = sin(B) / b = sin(C) / c

where A, B, and C are the angles of the triangle, and a, b, and c are the lengths of the sides opposite those angles.

Answer 2

Angles in a triangle add to
`180^(\circ)`.

`\angle B=180^(\circ)-115.5^(\circ)-27.2^(\circ) \longrightarrow \boxed{\angle B=37.3^(\circ)}`

Using the Law of Sines:

`(AC)/(\sin 37.3^(\circ))=(76.0)/(\sin 115.5^(\circ))\\\\\boxed{AC=(76\sin 37.3^(\circ))/(\sin 115.5^(\circ)) \text{ ft}}`

`(BC)/(\sin 27.2^(\circ))=(76.0)/(\sin 115.5^(\circ))\\\\\boxed{BC=(76\sin 27.2^(\circ))/(\sin 115.5^(\circ)) \text{ ft}}`