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Solving Right Triangle Side Lengths

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Questions and Answers

Which equation can be used to solve for C?

sin(50)=3/c (correct)

c=3/sin(50)

tan(50)=3/c

cos(50)=3/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?

tan(30)=5/b Signup and view all the answers

What is the correct equation to solve for b?

b=(8)tan(30) Signup and view all the answers

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

38.6 Signup and view all the answers

Which equation can be used to solve for C?

c=(5)cos(35) Signup and view all the answers

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.

23.1 inches Signup and view all the answers

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.

4.1 inches Signup and view all the answers

What is the length of CD?

10.7 cm Signup and view all the answers

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.