A cable is attached from the top of a tower to a point on the ground. If the tower is 50 meters tall and the cable makes a 60-degree angle with the ground, what is the length of the cable?

A ladder is leaning against a wall. The foot of the ladder is 4 feet away from the wall, and the ladder is 10 feet long. How high up the wall does the ladder reach? Use the Pythagorean Theorem to find the height.

A flagpole casts a shadow that is 15 feet long. The angle of elevation from the tip of the shadow to the top of the flagpole is 30 degrees. Using trigonometric ratios, find the height of the flagpole.

A person is looking at the top of a building. If the angle of elevation from the person to the top of the building is 45 degrees, and the person is standing 30 meters away from the base of the building, how tall is the building?

A bird is perched at the top of a 20-meter tall tree. If the angle of depression from the bird to a point on the ground is 60 degrees, how far is this point from the base of the tree?

An observer stands at a point 50 meters away from the base of a tower. If the angle of elevation from the observer to the top of the tower is 40 degrees, what is the height of the tower?

A boat is sailing directly away from a lighthouse. If the angle of elevation from the boat to the top of the 80-foot tall lighthouse changes from 30 degrees to 20 degrees, how far does the boat travel during this change?

A construction worker is looking at the top of a crane. From where he stands, 70 meters away from the base of the crane, the angle of elevation to the top is 35 degrees. How tall is the crane?

A man is flying a kite, and the string makes an angle of 50 degrees with the ground. If the length of the string is 100 meters, how high is the kite above the ground?

A rescue worker needs to determine the height of a cliff. They walk 60 meters away from the base of the cliff and measure the angle of elevation to the top to be 53 degrees. How tall is the cliff?