The angle of elevation from a point on the ground to the top of a tree is 38 degrees. The angle of elevation from a point 22.5 ft farther back to the top of the tree is 28.2 degrees. Find the height of the tree to 2 decimal places.
could you help me out..I got this so far..thanks
h/(tan38(=h/(tan28.2)29
 👍
 👎
 👁
 ℹ️
 🚩
1 answer

Make a sketch.
On the ground line, mark off the bottom of the tree as Q, your first position
as A and your second point further back as B.
Label the top of the tree as P
So we want to find PQ
In triangle PBA, we know angle PBA = 28.2° and angle PAQ = 142°,
which make angle APB = 9.8°
by the sine law:
22.5/sin9.8 = AP/sin28.2°
AP = 22.5 sin28.2/sin 9.8 = 62.4665... ( I stored that in memory)
In the righttriangle APQ
sin 38 = PQ/AP
PQ = APsin38 = 62.4665..(sin38) = 38.458..
= 38.46 ft 👍
 👎
 ℹ️
 🚩
answered by mathhelper
Answer this Question
Related Questions

MAT 150
At a point on the ground 70 feet from the base of the tree the distance the top of the tree is 2 feet more than three times the height of the tree find the height of the
 asked by Kimberly

Spherical Trigonometry
*100 meters from the base of the pine tree its top was sighted as forming 38 degrees with the ground.Find the height of the tree.
 asked by Bjorn

dynamic
A projectile fired from the edge of a 150 m high cliff with an initial velocity of 180 m/s at an angle of elevation of 30 deg with the horizontal. i. The greatest elevation above the ground reached by the projectile. ii. Horizontal distance from the gun to
 asked by Anonymous

Maths
The top of a building 24cm high is observed from the top and from the bottom of a vertical tree. The angles of elevation are found to be 45degree and 60degree respectively . Find the height of the tree. ( leave your answer in surd form)
 asked by Faith

MAT 150
At a point on the ground 15 feet from the base of a tree the distance to the top of the tree is 1 foot more than two times the height of the tree find the height of the tree
 asked by Kimberly

Math
An ant is on top of a tree 23 meters tall, directly above her home, which is 0.3 meters below the ground. What is an expression that represents the difference in elevation between the ant and her home?
 asked by Aubrey T.

trigonometry
A tree is broken over by the wind. It forms a right angled triangle with the ground. If the broken part makes an angle of 60° with the ground and the top of the tree is now 20m from its base, how tall WAS the tree?
 asked by MaThS

Math
Standing 4ft from the mirror lying on the ground ground, Palmer who's eye height is 5ft 9inches, can reflection the top of the tree. He measures the mirror to be 24ft from the tree. How tall is the tree?
 asked by Tan

trig
a building 60 feet high. from a distance at point A on the ground, the angle of elevation to the top of the building is 40 degree. from a little nearer at point B, the angle of elevation to the top of the building is 70 degree. What's the distance between
 asked by Anonymous

differential calculus
ANGLE OF ELEVATION A balloon rises at a rate of 4 meters per second from a point on the ground 50 meters from an observer.Find the rate of change of the angle of elevation of the balloon from the observer when the balloon is 50 meters above the ground.
 asked by =)

Mathematics
The top of a building 24cm high is observed from the top and from the bottom of a vertical tree .the angle of elevations are found to be 45 and 60 respectively find the height of the tree
 asked by Ujunwa

trigonometry
Solution of problem:from the top of a building 55 ft high, the angle of elevation of the top of a vertical pole is 12 degrees, At the bottom of the building, the angle of elevation of the top of the pole is 24 degrees. find the height of the pole.
 asked by alex

math
Sam and markus are standing on level ground 100m apart. A large tree is due north of markus and on a bearing of 65degrees from sam. The top of the tree appears at an angle of elevation of 25degrees to sam and 15degrees to markus. Find the height of the
 asked by putri

Mathematics
Calculate the height of a tree whose shadow is 20m shorter when the angle of elevation of the sun is 60° than when the angle of elevation is 30°
 asked by Olamide

Angles of elevation and depression
The teet of two vertical poles of height 3m and 7m are in line with a point P on the ground. The smaller pole being between the taller pole and P and at distance of 20m from P the angle of elevation of the top T of the taller pole from the top R of the
 asked by Emmanuel

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 determines that the angle
 asked by Tsunayoshi

trig
The angle relative to the horizontal from the top of a tree to a point 12 feet from its base(on flat ground) is 30*. Find the height of the tree.
 asked by rita

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

Math
The feet of two vertical poles of heights 3m and 7m are in line with a point P on the ground the smaller pole being between the taller pole and at a distance 20m from P.The angle of elevation of the top . T of the taller pole from the top R of the smaller
 asked by Foluke

trig
A survey team is trying to estimate the height of a mountain above a level plain. From one point on the plain, they observe that the angle of elevation to the top of the mountain is 24. From a point 1000 feet closer to the mountain along the plain, they
 asked by Anonymous
Still need help?
You can ask a new question or browse existing questions.