Question

Solve the triangle. round decimal answers to the nearest tenth. a triangle a b c with base a c is drawn. the length of side a b is 26 units. the measure of angle a c b is 81 degrees and the measure of angle b a c is 33 degrees.

Answer 1

Angles in a triangle add to
`180^(\circ)`, so
`\boxed{\angle ABC=66^(\circ)}`.

We can solve for the two side lengths using the law of sines.

`(BC)/(\sin 33^(\circ))=(26)/(\sin 81^(\circ))\\\\BC =(26 \sin 33^(\circ))/(\sin 81^(\circ))\\\\\boxed{BC \approx 14.3}\\\\\\(AC)/(\sin 66^(\circ))=(26)/(\sin 81^(\circ))\\\\AC=(26 \sin 66^(\circ))/(\sin 81^(\circ))\\\\\boxed{AC \approx 24.0}`