A
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°. How high is the tower?
414.2 m
The angle of elevation from a boat to the top of a 92-meter hill is 12°. How far is the boat from the base of the hill?
432.83 m
From the top of a cliff 280 meters high, the angle of depression of a boat is 25°. How far from the base of the cliff is the boat?
600.46 m
A ladder 8 meters long leans against the wall of a building. If the foot of the ladder makes an angle of 68° with the ground, how far is the base of the ladder from the wall?
3 m
Adrian is flying a kite. He is holding the end of the string at a distance of 1.5 m above the ground. If the string is 20 m long and makes an angle of 40° with the horizontal, how high is the kite above the ground?
14.36 m
A 12-meter high post casts a 19-meter shadow. Find the angle of elevation to the sun.
32.28 degrees
From an airplane at an altitude of 1200 m, the angle of depression to a rock on the ground measures 28°. Find the horizontal distance from the plane to the rock.
2,256.87 m
A four-meter ladder leans against a wall. If the foot of the ladder makes an angle of 80° with the ground, how high up the wall does the ladder reach?
3.94 m
The angle of elevation of the sun is 27° at the same time that a flagpole casts a shadow 12 m long. How high is the flagpole?
6.11 m
Obiwan is standing at a distance of 15 m from the base of a tree. From where he is standing, he can see the top of the tree. If the tree is 15 m high and Obiwan is 1 m tall, what is the angle of elevation of the top of the tree?
43.02 degrees
From the top of the control tower 250 m tall, an airplane is sighted on the ground below. If the airplane is 170 m from the base of the tower, find the angle of depression of the airplane from the top of the control tower.
55.78 degrees
A man, 1.5 m tall, is on top of a building. He observes a car on the road at an angle of 75°. If the building is 30 m high, how far is the car from the building?
8.44 m
From the top of a lighthouse 29.5 m high, the angle of depression of an observer to a boat is 28.5°. How far is the boat from the lighthouse?
54.33 m
A nursery plants a new tree and attaches a guy wire to help support the tree while its roots take hold. An eight foot wire is attached to the tree and to a stake in the ground. From the stake in the ground the angle of elevation of the connection with the tree is 42º. Find the height of the connection point on the tree.
5.4 ft.
From the top of a fire tower, a forest ranger sees his partner on the ground at an angle of depression of 40º. If the tower is 45 feet in height, how far is the partner from the base of the tower?
53.6 ft
An airplane took off from an airport and traveled at a constant rate and angle of elevation. When the airplane reached an altitude of 500 m, its horizontal distance from the airport was found to be 235 m. What was the angle when the airplane rose from the ground?
64.83 degrees
A ladder leans against a brick wall. The foot of the ladder is 6 feet from the wall. The ladder reaches a height of 15 feet on the wall. Find to the nearest degree, the angle the ladder makes with the wall.
22 degrees
A bamboo pole is leaning against a tree. If the height of the tree is 12.2 meters and the angle made by the pole and the ground is 40°, what is the length of the pole?
18.98 m
A man stands a top a building. He measures the angle of elevation to the building across the street to be 27° and the angle of depression (to the base of the building across the street) to be 31°. If the two buildings are 50 feet apart, how tall is the taller building?
55.5 ft.
Find the shadow cast by a 10 foot lamp post when the angle of elevation of the sun is 58º. Find the length of a foot.
6.2 ft.
An observer in a lighthouse 48.8 m above sea level saw two vessels moving directly towards lighthouse. He observed that the angles of depression are 42° and 35°. Find the distance between the two vessels, assuming that they are coming from the same side of the tower.
15.49 m
According to a lighting specialist for an art gallery, for best illumination of a piece of art, it is recommended that a ceiling mounted light be 1.8 m from the piece of art and that the angle of depression of the art piece be 38°. How far from the wall should the light be placed so that the recommendations of the specialist are met?
1.4 m
A radio station tower was built in two sections. From a point 87 feet from the base of the tower, the angle of elevation of the top of the first section is 25º, and the angle of elevation of the top of the second section is 40º. To the nearest foot, what is the height of the top section of the tower?
32 ft
Buildings A and B are across the street from each other, 35m apart. From a point on the roof of Building A the angle of elevation at the top of Building B is 24°, and the angle of depression of the base of Building B is 34°. How tall is each building?
39.2 m
If a man is just about to ski down a steep mountain. He estimates the angle of depression from where he is now to the flag at the bottom of the course to be 24°. He knows that he is 800 feet higher than the base of the course. How long is the path that he will ski?
1,966.87 ft.