Trigonometry Quiz

Multiple Choice

1. What is the formula for the Law of Sines?

   • A. sin(A) = sin(B)
   • B. sin(A) = cos(B)
   • C. sin(A)/a = sin(B)/b = sin(C)/c
   • D. sin(A) = tan(B)

2. What is the measure of an angle in a right triangle if the two sides are 6 and 8?

   • A. 30°
   • B. 45°
   • C. 60°
   • D. 90°

3. What is the formula for the area of a triangle?

   • A. (a + b + c)/2
   • B. (a + b)/2
   • C. a x b
   • D. 1/2 x b x h

True or False

1. The Law of Cosines can be used to find the measure of a missing angle in a triangle.

   • A. True
   • B. False

2. The Law of Sines is used to calculate the area of a triangle.

   • A. True
   • B. False

3. The Pythagorean Theorem is used to calculate the measure of a missing angle in a triangle.

   • A. True
   • B. False

Fill in the Blank

1. The ___________ Theorem states that the sum of the squares of the two shorter sides of a right triangle is equal to the square of the hypotenuse.

2. The __________ is a ratio of the sides of a right triangle.

3. The _________ of a triangle is the measure of the angle opposite the longest side.

Short Answer

1. What is the Law of Cosines and how is it used?

2. What is the Pythagorean Theorem and how is it used?

3. What is the difference between the Law of Sines and the Law of Cosines?

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Trigonometry Practice Sheet

Introduction

Trigonometry is an important branch of mathematics that studies the relationships between angles and sides of triangles. It is used in many areas of mathematics, engineering, and science. This practice sheet will help you understand the basics of trigonometry and give you an opportunity to practice solving problems.

Basic Trigonometry

Angles

An angle is a measure of rotation. The most common unit of measure for angles is degrees.

A right angle is an angle with a measure of 90°.

An acute angle is an angle with a measure of less than 90°.

An obtuse angle is an angle with a measure of more than 90°.

Trigonometric Ratios

Trigonometric ratios are ratios of two sides of a right triangle.

The three main trigonometric ratios are:

• sine (sin): the ratio of the length of the side opposite an angle to the length of the hypotenuse
• cosine (cos): the ratio of the length of the side adjacent to an angle to the length of the hypotenuse
• tangent (tan): the ratio of the length of the side opposite an angle to the length of the side adjacent to an angle

Solving Right Triangles

To solve a right triangle, you will need to know either two sides or one side and one angle.

If you know two sides, you can use the Pythagorean Theorem to find the third side.

If you know one side and one angle, you can use the trigonometric ratios to find the other sides.

Practice Problems

1. Find the measure of the angle in the right triangle below:

Answer: 90°

1. Find the length of side AB in the right triangle below:

Answer: 10

1. Find the length of side AC in the right triangle below:

Answer: 8

Answer Key

1. 90°
2. 10
3. 8