## Questions and Answers

Which equation can be used to solve for C?

The relationship sin(b)=cos(90-b) in a triangle is always true.

True

What is the length of AC? Round to the nearest tenth.

10.5 m

Which equation can be used to solve for b?

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What is the correct equation to solve for b?

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What is the length of AB? Round to the nearest tenth.

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Which equation can be used to solve for C?

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What is the best estimate for the perimeter of a triangle with angles measuring 30°, 60°, and 90° and a hypotenuse of 10 inches? Round to the nearest tenth.

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What is the length of the hypotenuse of a right triangle that has one side measuring 4 inches and an opposite angle of 80°? Round to the nearest tenth.

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What is the length of CD?

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## Study Notes

### Right Triangle Relationships and Calculations

- To find the side length C, use the equation: sin(50) = 3/c.
- The relationship between angles in a right triangle is expressed as sin(b) = cos(90-b).

### Side Length Calculations

- Length of side AC is approximately 10.5 m when rounded to the nearest tenth.
- To solve for side b, the equation tan(30) = 5/b can be applied.
- An alternative equation for b is b = 8 * tan(30).

### Additional Side Length Information

- The length of side AB is approximately 38.6 when rounded to the nearest tenth.
- Equations to find C include c = 5 * cos(35) and c = 5 * sin(35).

### Triangle Properties

- In a triangle with angles measuring 30°, 60°, and 90°, and a hypotenuse of 10 inches, the estimated perimeter is around 23.1 inches when rounded to the nearest tenth.
- For a right triangle with one side measuring 4 inches and an opposite angle of 80°, the hypotenuse is approximately 4.1 inches when rounded to the nearest tenth.

### Side Length D

- The length of side CD is measured to be 10.7 cm.

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## Description

This quiz focuses on solving for the side lengths of right triangles using trigonometric functions. Each card presents a question that tests your understanding of sine, cosine, and tangent relationships. Review these concepts to enhance your skills in geometry and trigonometry.