# Math - Trigonomety

A plane is flying at a height of 1000 feet. A passenger on the plane sees a tree and realizes the angle of depression to the top of the tree is 15 degrees and the angle of depression to the bottom of the tree is 25 degrees. How tall is the tree?

1. 👍 0
2. 👎 0
3. 👁 226
1. What a silly and unrealistic problem,
anyway ....

the main working triangle has the height of the tree, its opposite angle as 10°, and the other angles as 105° and 65°
The side opposite the 105° is also the hypotenuse of a right-angled triangle with vertical side 1000 and base angle 25° (alternate angle to your angle of depression)
let that hypotenuse be h
sin25 = 1000/h
h = 1000/sin25 = 2366.2

now in the other triangle, by the sine law
tree/sin10 = 2366.2/sin105
tree = 2366.2sin10/sin105 = 425.4 ft

wow !

Since the tallest trees in the world, the sequoias of the west coast all are less than 400 ft ..........

1. 👍 0
2. 👎 0

## Similar Questions

1. ### Physics

Two planes are about to drop an empty fuel tank. At the moment of release each plane has the same speed of 135 m/s, and each tank is at the same height of around 2.00km above the ground. Although the speeds are the same, the

2. ### math

A plane is flying at 32,460 feet. To avoid some turbulence, the plane ascends 1645 feet. It then descends 3 5 of its new height to prepare for landing. What are the heights that the plane will be at after it ascends to avoid

3. ### Math

Me, again... Please help me. Thank you. Assume a plane is flying directly north at 200 mph, but there is a wind blowing west at 23 mph. Part I: Express both the velocity of the plane and the velocity of the wind as vectors, using

4. ### Math

Have you ever been on an airplane and heard the pilot say that the plane would be a little late because it would be flying into a strong headwind or that even though the plane was taking off a bit late, you would be making up time

1. ### math

an airplane is flying at a height of 2 miles above the level ground. the angle of depression from the plane to the foot of a tree is 15 degree. Find the distance that the plane must fly to be directly above the tree.

2. ### PHYSICS

Two planes fly from toronto to philadelphia. Plane a flies via pittsburgh whereas passenger on plane B have a direct flight. Pittsburgh is 350km due south of Toronto and 390km due west of Philadelphia. The airspeed of both planes

3. ### maths

A plane is flying at 31,348 feet. It needs to rise to 36,000 feet in two stages. In stage 1, it rises 5% of its initial altitude of 31,348 feet. In stage 2, it rises at a rate of 140.3 feet per minute. How many minutes does it

4. ### physics

A plane is found by radar to be flying 5.9 km above the ground. The angle of elevation from the radar to the plane is 78.6°. Ten seconds later, the plane is directly over the station. Find the speed of the plane, assuming that it

1. ### Pre-calc

The Blue Angels, the Navy's elite flying squadron, have performed for more than 427 million fans since their inception in 1946. Suppose the two Blue Angel jets at points P and A in the diagram have elevations of 1555 feet and 1000

2. ### geometry

An observer (O) spots a plane flying at a 55° angle to his horizontal line of sight. If the plane is flying at an altitude of 21,000 ft., what is the distance (x) from the plane (P) to the observer (O)?

3. ### Trigonometry

A passenger in an airplane flying at an altitude of 10 kilometers sees two towns directly to the left of the plane. The angles of depression to the towns are 28° and 55°. How far apart are the towns?

4. ### math

Two planes leave simultaneously from Chicago's O'Hare Airport, one flying due north and the other due east. The northbound plane is flying 50 miles per hour faster than the eastbound plane. After 3 hours the planes are 2840 miles