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Trig Practice Problems For each problem you MUST o draw & label a sketch o show your set up equation o show all work for the solution 1. Rudy is standing 50 feet away from the base of a large tree. The angle of elevation from Rudy‟s eyes to the top of the tree is 53o. Rudy‟s eyes are 5 feet 8 inches off the ground. How tall is the tree? 2. A pilot estimates that the angle of depression from his air position to the top of a skyscraper is 7o. His horizontal distance from the building is 10,000 ft. If he maintains the current cruising altitude, how high above the building will the plane be when it passes over? 3. A lighthouse is perched on the edge of a cliff. A sailor is on a ship 100 ft from the base of the cliff. The angle of elevation from the eyes of the sailor to the top of the lighthouse is 50o. How far from the sailor is the top of the lighthouse? 4. Bobby is flying a kite. A very frightened spider is hanging on to the kite for dear life with all 8 of its legs. The spider notices that the angle of depression from his location on the kite to the roll of string in Bobby‟s hand is 40o. If the height of the kite is 50 ft higher than the roll of string, how much string would our very frightened spider have to traverse to reach the roll of string & therefore relative safety (if Bobby doesn‟t just “smoosh” him when he gets there!) 5. A blimp is flying 500 ft above the ground. A person on the ground sees the blimp by looking at a 25o angle. The person„s eye level is 5 ft above the ground. Find the distance from the blimp to the person. 6. In a sightseeing boat near the base of the Horseshoe Falls at Niagara Falls, a passenger estimates the angle of elevation to the top of the falls to be 30o. If the Horseshoe Falls are 173 ft high, what is the distance from the boat to the base of the falls? 7. A surveyor stands 100 ft from a building and sights the top of the building at a 55o angle of elevation. Find the height of the building. 8. A geologist measured a 40o angle of elevation to the top of a mountain. After moving 0.5 km farther away, the angle of elevation was 34o. How high is the top of the mountain? (Hint: use 2 variables, one for the height of the mountain, h, and one for distance from first measurement, x. The distance from the second measurement will be in terms of x. Solve both equations for x & set the expressions equal to each other) 9. Find the height of an isosceles trapezoid with base angle of 38o and legs of 25 inches. 10. A sonar operator on a cruiser detects a submarine at a distance of 500 m and an angle of depression of 37o. How deep is the sub? 11. Find to the nearest degree, the angles of a 3 - 4 - 5 triangle. 12. Two buildings are 100 feet apart across a street. A sunbather at the edge of the roof of the shorter building finds the angle of elevation to the roof of the taller building to be 25o and the angle of depression to its base to be 30o. Find the height of the taller building to the nearest foot.
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