# A flagpole sits on the top of a building. Angles of elevation are measured from a point #500# feet away from the building. The angle of elevation to the top of the building is #38˚# and to the top of the flagpole #42˚#. How high is the flagpole?

##### 2 Answers

The height of the flagpole is approximately

#### Explanation:

Always try to draw a diagram.

We know that there is a right angle between the ground and the building. Therefore, we can use the 3 basic trig ratios instead of the sine or cosine law to solve this problem.

Since the angle in the corner of the larger right triangle measures

By basic trig ratios, we can find the height of the building with the flag pole on top, call it

#(tan42˚)/1 = H/500#

#H = 500tan42˚#

I would keep it in exact form until the last step.

We now devise an expression for the height of the building (without the flag pole). Call it

#(tan38˚)/1 = a/500#

#a = 500tan38˚#

We can now state that

#h = H - a#

#h = 500tan42˚ - 500tan38˚#

#h ~~ 59.559 ~~ 60 "feet"#

Hopefully this helps!

The flagpole is

#### Explanation:

1) The flagpole is on top of a building.

2)Angles of elevation both measured from point

3) Angle of elevation to the top of building is

4) Angle of elevation to the top of flagpole is

The information above will provide us with two right angle triangles, one smaller one inside a larger one.

Both will have a **base** of

The smaller triangle will have a base angle

From this information we can find the heights of the building and the building + pole using the definition of the **tangent** of the two base angles

Then to the nearest foot the height of the flagpole is: