CPM Homework Help : INT2 Problem 4-29

Salvador has a hotdog stand $58$ meters from the base of the Space Needle in Seattle. He prefers to work in the shade and knows that he can calculate when his hotdog stand will be in the shade if he knows the height of the Space Needle. To measure its height, Salvador stands at the hotdog stand, gets out his clinometer, and measures the angle to the top of the Space Needle to be $80^{\circ}$ . Salvador’s eyes are $1.5$ meters above the ground. Assuming that the ground is level between the hotdog stand and the Space Needle, how tall is the Space Needle?

Hint:

Sketch a diagram to help visualize the problem.

Help:

Use the tangent ratio with a variable for the vertical distance between Salvador's eye sight and the top of the Space Needle.

Rectangle, left side labeled 1.5 m, right side is dashed segment, top side labeled 58 m, Right triangle with horizontal leg on top side of rectangle, & vertical leg extended up from right rectangle side, angle opposite vertical leg labeled 80 degrees, top right vertex is top of space needle.