# math

posted by .

A radio tower stands on the top of a hill that is 85 feet high. From the bottom of the hill, the elevation angle to the base of the tower is 42 degrees and the elevation angle to the top of the tower is 60 degrees. How tall is the tower?
I would like to know what steps to take to arrive at this answer.

• math -

Step 1:
Draw a diagram, with a tower of height h on top of a hill 85' hight.
The 42° angle of elevation is measured at a horizontal distance x from the base of the tower.
Step 2:
Calculate x knowing that tan(42)=85/x
Step 3:
Calculate h knowing that
tan(60)=(85+h)/(x)
Step 4:
Solve for h.

## Similar Questions

1. ### Math

to measure the height of the Eiffel Tower in Paris, a person stands away from the base and measures the angle of elevation to the top of the tower to be 60 degrees. Moving 210 feet closer, the angle of elevation to the top of the tower …
2. ### precalculus

A radio tower is located 450 feet from a building. From a window in the building, a person determines that the angle of elevation to the top of the tower is 29 degrees and that the angle of depression to the bottom of the tower is …
3. ### math

A tower 125 feet high stands on the side of a hill. At a point 240 feet from the foot of the tower measured straight down the hill, the tower subtends an angle of 25 degrees. What angle does the side of the hill make with the horizontal?
4. ### math

A tower 125 feet high stands on the side of a hill. At a point 240 feet from the foot of the tower measured straight down the hill, the tower subtends an angle of 25 degrees. What angle does the side of the hill make with the horizontal?
5. ### math

A tower 125 feet high stands on the side of a hill. At a point 240 feet from the foot of the tower measured straight down the hill, the tower subtends an angle of 25 degrees. What angle does the side of the hill make with the horizontal?
6. ### Math

1. A rangers tower is located 44m from a tall tree. From the top of the tower, the angle of elevation to the top of the tree is 28 degrees and the angle of depression to the base is 36 degrees. How tall is the tree?
7. ### Math

If an observer stands at a certain point in the same horizontal plane as the base of a radio tower. the angle of elevation of the top of the tower is 13deg 15'. If the observer moves 156.25 feet towards the tower, the angle of elevation …
8. ### trig

On an inclined road, which makes an angle of 25 degrees with the horizontal plane, stands a vertical tower. At a point Q, 150 ft from the base of the tower down the road, the angle of elevation to the top of the tower is 65. How high …
9. ### physics

1) The angle of elevation to the bottom of a transmission tower on a hill from an observer standing 1.8 km away from the base of the hill is 5 degrees. The angle of elevation to the top of the tower from the tower is 6.8 degrees. If …
10. ### math

A hiker is 400 meters away from the base of the radio tower. The angle of elevation to the top of the tower is 46 degrees . How high is the tower?

More Similar Questions