I dont know how to do this

Question

Joy is standing on the 40 foot cliff overlooking a river. The angle of depression to the near side of the river is 64°, and the angle of depression to the far side is 35°. How wide is the river,to the nearest 10th of a foot?

Answer 1

Draw and label a diagram:

 

A is the point at which Joy is standing

B is the point directly below on the bank of the river.

Draw a line perpendicular to AB. Label the end B (this is the width of the bank "b."

Continue the line to a point D. BD = r the width of the river.

 

m∠CAB = 26° (90° - 64°)

m∠CAD = 55° (90° - 35°)

 

tan 26° = b/40

40tan26° = b

40(0.488) = b

19.52 = b

 

tan55° = (19.52 + r) / 40

40tan55° = 19.52 + r

40(1.428) = 19.52 + r

57.13 = 19.62 + r

37.50 = r