Right Triangle Word Problems
Solve real-world problems involving right triangles using the Pythagorean theorem and trigonometric ratios.
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Right Triangle Word Problems
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Read each word problem carefully and solve for the unknown. Show all your work. Round your answers to two decimal places where necessary.
1. A ladder is leaning against a wall. The top of the ladder reaches 12 feet up the wall. The base of the ladder is 5 feet away from the wall. How long is the ladder?
2. A rectangular park is 8 miles long and 6 miles wide. If you walk diagonally across the park, how far do you walk?
3. The angle of elevation from a boat to the top of a lighthouse is 25 degrees. If the lighthouse is 100 feet tall, how far is the boat from the base of the lighthouse? (Hint: Use tangent)
Answer: The boat is approximately feet from the lighthouse.
4. A kite is flying at an angle of elevation of 40 degrees. The string is 75 meters long. How high is the kite above the ground? (Hint: Use sine)
Answer: The kite is approximately meters high.
5. A ramp is 15 feet long and rises 3 feet vertically. What is the angle of elevation of the ramp to the nearest degree?
11.54 degrees
11.31 degrees
11.75 degrees
12.00 degrees
6. A person standing 20 meters from the base of a tree observes the angle of elevation to the top of the tree to be 45 degrees. How tall is the tree?
10 meters
15 meters
20 meters
25 meters
7. A flagpole casts a shadow 30 feet long. The angle of elevation from the end of the shadow to the top of the flagpole is 50 degrees. What is the height of the flagpole?
8. From the top of a 70-foot cliff, the angle of depression to a boat is 20 degrees. How far is the boat from the base of the cliff?
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