Right Triangle Word Problems Worksheet
This worksheet focuses on solving real-world problems using the principles of right triangles, including the Pythagorean theorem and trigonometric ratios.
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Right Triangle Word Problems
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Read each problem carefully, draw a diagram if helpful, and use the Pythagorean theorem or trigonometric ratios (sine, cosine, tangent) to solve. Show all your work.
1. A ladder is leaning against a wall. The top of the ladder reaches 12 feet up the wall. If the base of the ladder is 5 feet away from the wall, how long is the ladder?
2. A kite is flying at an angle of elevation of 40° from the ground. If the string to the kite is 100 feet long, how high is the kite above the ground?
3. A boat travels 15 miles east and then 8 miles north. The shortest distance from the boat's starting point to its current position is miles.
4. If a right triangle has legs of length 6 and 8, its hypotenuse must be 10.
True
False
5. A flagpole casts a 24-foot shadow when the angle of elevation of the sun is 60°. What is the approximate height of the flagpole?
13.86 feet
24 feet
41.57 feet
48 feet