Question

Solve AABC. Round your answers to the nearest hundredth, if necessary

Answer 1

`C=25^(\circ),\\a\approx 10.72,\\b\approx 11.83`

Explanation:

The sum of the interior angles of a triangle is 180 degrees. Thus, angle C must be
`180-90-65=25^(\circ)`.

In any triangle, the Law of Sines is given by
`(\sin A)/(a)=(\sin B)/(b)=(\sin C)/(c)`.

Therefore, we have:

`(\sin 90^(\circ))/(b)=(\sin 25^(\circ))/(5),\\\\b=(5\sin90^(\circ))/(\sin 25^(\circ))=11.8310079158\approx \boxed{11.83}`

`(a)/(\sin 65^(\circ))=(5)/(\sin25^(\circ)),\\a=(5\sin 65^(\circ))/(\sin25^(\circ))=10.7225346025\approx \boxed{10.72}`