another bearings question

Question

From the top of a tower of height 75m, a guard sees two prisoners both due west of him. if the angles of depression of the two prisoners are 10 and 17 degrees, calculate the distance between them.

Answer 1

Hi Ash,

 

It helps to draw a right triangle with the 75 meter tower being the vertical leg and the horizontal line being the distance to the prisoner.  The angle between that line and the hypotenuse is given in the problem.  Since the horizontal line is the adjacent side and the tower is the opposite side, you'll need to find the tangent of the angle with your calculator.

 

Tan 10 = 75 / distance to first prisoner

 

Tan 17 = 75 / distance to the second prisoner.

 

Have fun.

 

Dan