A woman entering an outside glass elevator

Question

A woman entering an outside glass elevator on the ground floor of a hotel glances up to the top of the building across the street and notices that the angle of elevation is 53°. She rides the elevator up three floors (60 feet) and finds that the angle of elevation to the top of the building across the street is 34°. How tall is the building across the street

Answer 1

Draw a figure!

Label the entrance to the hotel O and the top of the building across the street C.

Draw a vertical line 60' tall to point A and a horizontal line from A which intersects OC at B.and the building at D.

Length of AB is 60/tan 53

In triangle ABC the angle at A is 34°, at B is 127° (supplemental to 53°) and at C is 19°.

Now use the law of sines to get BC, the hypotenuse of triangle BCD.

The length DC = BC * sin 53.

The height of the bldg is 60+DC