Triangle Angle of Elevation Problem...

Question

The Sears Tower in Chicago is 1,454 feel tall and is located about 1 mile inland from the shore of Lake Michigan. An observer in a rowboat on the lake measures the angle of elevation to the top of the tower as 4 degrees. To the nearest foot, how far offshore is the rowboat?

 

Please show all the steps involved in solving this problem.

The following choices are provided for answers:

A.) 4,917 feet

B.) 15,513 feet

C.) 20,793 feet

D.) None of the above

Answer 1

you will have to use a little trigonometry to solve this problem as you have a right triangle ABC

let X = the distance from the vertex B to the boat, then X -5280 = distance from the shore to the boat

then use a function of either the 4^o angle or the 86^o angle to compute the answer.

Answer 2

B) 15513 ft.

 

tan 4 degrees = (1454) / (5280  + x)

 

1454 is the height of the building.

5280 ft per mile

x is the offshore distance.

 

Solve for x!