Trig word problem

Question

From a point 25m far from a building the angle of elevation to the fifth floor is 26 degrees while the angle of elevation to the top of the building is 67 degrees. What is the distance between the fifth floor and the top of the building?

Answer 1

You have a baseline and you need a height, which means you will want to use the tangent function to find the relation between the baseline and the height without calculating the distance (the hypotenuse).

 

the height of the fifth floor

25m (tan26º) = 12.19m

 

the height of the roof

25m (tan67º) = 58.90m

 

distance between top and fifth floor

d = 58.90m - 12.19m = 46.71m