# math

From a lookout tower 80 ft. high, a man observes from a position 6.5 ft. below the top of the tower that the angle of elevation of the top of a certain tree is 12 degrees 40 minutes and the angle of depression of its base is 72 degrees 20 minutes. If the base of the tower and the base of the tree are at the same level, what is the height of the tree?

1. 👍 0
2. 👎 0
3. 👁 506
1. If you draw a diagram, you will see that you cannot compute the height of the tree without knowing how far apart are the tower and the tree.

1. 👍 0
2. 👎 0
2. The observer is 80-6.5=73.5 above the base of the tower and the base of the tree.

An angle of depression to the base of the tree of 72-20-00 means that the distance between the tower and the tree is D=73.5/tan(72-20-00)
the difference between the top of the tree and the observer is therefore
h=D sin(12-40)

The height of the tree, H, is then
H=73.5+D sin(12-40)
=73.5 + 73.5 sin(12-40-00)/tan(72-20-00)
=73.5(1+sin(12-40-00)/tan(72-20-00))
=78.6 ft

1. 👍 0
2. 👎 0
3. ewqwqe

1. 👍 0
2. 👎 0

## Similar Questions

1. ### Trigonometry

At a point on the ground 125 ft from the base of a tower, the angle of elevation to the top of the tower has a degree measure of 38 degrees. How high is the tower

asked by Claire on April 23, 2016
2. ### Calculus

The CN Tower is 553 m tall. A person is south of the tower, in a boat on Lake Ontario at a position that makes an angle of elevation of 100 degrees to the top of the tower. A second person is sitting on a park bench, on a bearing

asked by Anonymous on May 23, 2010
3. ### math calc

A water tower is located 354 feet from a building. From a window in the building, an observer notes that the angle of elevation to the top of the tower is 42° and that the angle of depression to the bottom of the tower is 20°.

asked by Michael on April 21, 2015
4. ### math

Two lookout stations, which are 25 miles apart along the coast on a north-south line, spot an approaching yacht. One lookout station measures the direction to the yacht at N 33degrees E, and the other station measures the

asked by kai on December 11, 2012
5. ### Pre-Calc

The CN Tower in Toronto, Canada, is the tallest free-standing structure in North America. A woman on the observation deck, 1150 ft above the ground, wants to determine the distance between two landmarks on the ground below. She

asked by Susan on November 19, 2015
1. ### 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? 2. An engineer

asked by Tsunayoshi on February 6, 2014
2. ### geometry

A radio tower casts a shadow 170 feet long. The angle of elevation of the sun is 43 degrees. How high is the tower? Round to hundredths.

asked by Anonymous on February 26, 2013
3. ### science

An object fired horizontally with a velocity of 30m/s from a top of a taal tower 250m high.The object lands on top of a building which is 174m away from the tower.How high is the building.(g=10m/s^2)

asked by KESSE on May 5, 2019
4. ### trigonometry

From lookout tower 80ft. high, a man observes from a position 6.5 ft. below the top of the tower that the angle of elevation of the top of the certain tree is 12deg40mins and the angle of depression of its base is 70deg20mins. If

asked by Winsel on August 14, 2010
5. ### Trigonometry

frrom outlook tower 80ft. high, a man observes from a position 6.5ft. below the top of the tower that the angle of elevstion of the top of certain tree is 12deg40mins and the angle of depression of its base is 72deg20mins. If the

asked by Winsel on August 10, 2010