Lesson 5
Working with Ratios in Right Triangles
Problem 1
A triangle has sides with lengths 8, 15, and 17.
- Verify this is a Pythagorean triple.
- Approximate the acute angles in this triangle.
Solution
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Problem 2
Kiran is flying a kite. He gets tired, so he stakes the kite into the ground. The kite is on a string that is 18 feet long and makes a 30 degree angle with the ground. How high is the kite?
![String = hypotenuse = 18 feet. angle with the ground = 30 degrees. Perpendicular height unknown.](https://staging-cms-im.s3.amazonaws.com/kgaRX1Eu4y56u79kFtboFCP7?response-content-disposition=inline%3B%20filename%3D%2230%20degree.png%22%3B%20filename%2A%3DUTF-8%27%2730%2520degree.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240703%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240703T083321Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=3181c564bc4bdc77753db9864f632a601ff5dc1042f524d4a3294831c346bff8)
Solution
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Problem 3
Triangle \(ABC\) has a right angle at \(C\). Select all measurements which would mean it has a hypotenuse with a length of 10 units.
Angle \(A\) is 20 degrees, \(BC\) is 2 units
\(AC\) is 7 units, \(BC\) is 3 units
Angle \(B\) is 50 degrees, \(BC\) is 4 units
Angle \(A\) is 30 degrees, \(BC\) is 5 units
\(AC\) is 8 units, \(BC\) is 6 units
Solution
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Problem 4
What is a reasonable approximation for angle \(B\) if the ratio of the adjacent leg divided by the hypotenuse is 0.45?
27 degrees
30 degrees
60 degrees
63 degrees
Solution
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(From Unit 4, Lesson 4.)Problem 5
Estimate the values to complete the table.
angle | adjacent leg \(\div\) hypotenuse | opposite leg \(\div\) hypotenuse | opposite leg \(\div\) adjacent leg |
---|---|---|---|
\(A\) | 0.31 | 0.95 | 3.1 |
\(C\) |
Solution
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(From Unit 4, Lesson 4.)Problem 6
What is the length of side \(AB\)?
Solution
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(From Unit 4, Lesson 3.)Problem 7
What is the length of the square’s side?
3 units
\(\frac{6}{\sqrt2}\) units
\(6 \sqrt2\) units
12 units
Solution
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Problem 8
Find the lengths of segments \(AD\) and \(BD\). Then check your answers using a different method.
Solution
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(From Unit 3, Lesson 13.)