cASEY SIGHTS THE TOP OF AN 84 FOOT TALL LIGHTHOUSE AT AN ANGLE OF ELEVATION OF 58 DEGREE. IF CASEY IS 6 FEET TALL, HOW FAR IS HE STANDING FROM THE BASE OF THE LIGHTHOUSE.

I DO NOT UNDERSTAND WHAT IS ANGLE OF ELEVATION CAN YOU SHOW ME AN EXAMPLE PLEASE THANK YOU.

3 answers

draw a diagram. If you label

T = top of lighthouse
B = base of lighthouse
C = Casey

then the angle of elevation is the angle BCT

That is, 0° is a horizontal line of sight, meaning that he has to look up at an angle of 58° to see the top of the lighthouse.

So, using you basic trig functions, and assuming that Casey's eyes are at the top of his head, then the part of the lighthouse above Nick's eyes (84-6 feet), sets up our triangle

(84-6)/x = tan 58°

Now just solve for x, the distance of Casey from B.

tan 58 78/x - 78/tan 58

48.7