Right Triangle Trigonometry Word Problems

Angle of Elevation- Angle created by a horizontal surface and the hypotenuse. Ex. The angle of elevation of the top of a pole measures 48° from a point on the ground 18 ft away from its base. Find the height of the flagpole.

Example 1 A 6ft man casts a shadow. If the angle of elevation to the sun is 33°, how long is the shadow?

Ex 2: Length of a Building’s Shadow An 850-foot tall building casts a shadow of length L when the sun is θ° above the horizon. Write L as a function of θ. Complete the table below. θ 10° 20° 30° 40° 50° L

Ex 3: Drive-in Movie You are 50 feet from the screen at a drive-in movie. Your eye is on a horizontal line with the bottom of the screen and the angle of elevation to the top of the screen is 58°. How tall is the screen?

Ex. 4 Depth of a Submarine The sonar of a navy cruiser detects a nuclear submarine that is 4000 feet from the cruiser. The angle between the water level and the submarine is 32°. How deep is the submarine?

Ex 5: Airplane Ascent When an airplane leaves the runway, its angle of climb is 18° and its speed is 275 feet per second. Find the plane’s altitude after 1 minute.

Ex 6: Skyscraper You are a block away from a skyscraper that is 780 ft tall. Your friend is between the skyscraper and yourself. The angle of elevation from your position to the top of the skyscraper is 42°. The angle of elevation from your friend’s position to the top of the skyscraper is 71°. To the nearest foot, how far are you from your friend?