Grade: Grade 10 Subject: Mathematics Unit: Trigonometry Basics Lesson: 6 of 6 SAT: Geometry+Trigonometry ACT: Math

Unit Quiz

Test your understanding of trigonometry basics. Complete all 12 questions, then check your answers.

Quiz Instructions

  • Time: Aim to complete this quiz in 20-25 minutes
  • Calculator: You may use a calculator (make sure it's in degree mode!)
  • Show your work: Write out your steps before checking answers
  • Scoring: Each question is worth 1 point (12 points total)
  • Passing: 9/12 (75%) demonstrates proficiency

Tip: Work through all problems first, then reveal answers at the end to simulate a real test experience.

Quiz Questions

Question 1: Basic Ratio Identification

In a right triangle, angle A has an opposite side of 5 and a hypotenuse of 13. What is sin(A)?

Your answer: _______________

Question 2: Basic Ratio Calculation

In a right triangle, angle B has an adjacent side of 8 and a hypotenuse of 17. What is cos(B)?

Your answer: _______________

Question 3: Finding a Side Using Sine

In right triangle XYZ, angle X = 42 degrees and the hypotenuse is 15 cm. Find the length of the side opposite to angle X. Round to two decimal places.

Your answer: _______________ cm

Question 4: Finding a Side Using Cosine

In right triangle PQR, angle P = 28 degrees and the hypotenuse is 20 meters. Find the length of the side adjacent to angle P. Round to two decimal places.

Your answer: _______________ meters

Question 5: Finding a Side Using Tangent

In a right triangle, angle A = 55 degrees and the side adjacent to angle A is 12 units. Find the side opposite to angle A. Round to two decimal places.

Your answer: _______________ units

Question 6: Finding an Angle Using Inverse Sine

In a right triangle, the opposite side is 7 and the hypotenuse is 25. Find the angle (in degrees). Round to two decimal places.

Your answer: _______________ degrees

Question 7: Finding an Angle Using Inverse Tangent

In a right triangle, the opposite side is 9 and the adjacent side is 12. Find the angle (in degrees). Round to two decimal places.

Your answer: _______________ degrees

Question 8: Word Problem - Ladder

A 25-foot ladder leans against a building, making a 72-degree angle with the ground. How high up the building does the ladder reach? Round to two decimal places.

Your answer: _______________ feet

Question 9: Word Problem - Shadow

A telephone pole casts a shadow 35 feet long when the sun's angle of elevation is 48 degrees. How tall is the telephone pole? Round to two decimal places.

Your answer: _______________ feet

Question 10: Word Problem - Angle of Depression

From the top of a 60-meter lighthouse, a keeper spots a boat at an angle of depression of 22 degrees. How far is the boat from the base of the lighthouse? Round to the nearest meter.

Your answer: _______________ meters

Question 11: Pythagorean Identity

If cos(theta) = 3/5, and theta is an acute angle, what is sin(theta)? Express as a fraction.

Your answer: _______________

Question 12: Complete Triangle Solution

In right triangle ABC with right angle at C, side a = 8 cm (opposite angle A) and side b = 15 cm (opposite angle B). Find:

  • The hypotenuse c
  • Angle A (in degrees, rounded to two decimal places)

Your answers: c = _______________ cm, angle A = _______________ degrees

Answer Key

Check your answers after completing all questions.

Reveal All Answers

Question 1

Answer: 5/13 or approximately 0.385

sin(A) = opposite/hypotenuse = 5/13

Question 2

Answer: 8/17 or approximately 0.471

cos(B) = adjacent/hypotenuse = 8/17

Question 3

Answer: 10.04 cm

sin(42) = opposite/15

opposite = 15 * sin(42) = 15 * 0.6691 = 10.04 cm

Question 4

Answer: 17.66 meters

cos(28) = adjacent/20

adjacent = 20 * cos(28) = 20 * 0.8829 = 17.66 meters

Question 5

Answer: 17.14 units

tan(55) = opposite/12

opposite = 12 * tan(55) = 12 * 1.4281 = 17.14 units

Question 6

Answer: 16.26 degrees

sin(angle) = 7/25 = 0.28

angle = sin^(-1)(0.28) = 16.26 degrees

Question 7

Answer: 36.87 degrees

tan(angle) = 9/12 = 0.75

angle = tan^(-1)(0.75) = 36.87 degrees

Question 8

Answer: 23.78 feet

The height is opposite to the 72-degree angle, ladder is the hypotenuse.

sin(72) = height/25

height = 25 * sin(72) = 25 * 0.9511 = 23.78 feet

Question 9

Answer: 38.88 feet

The pole height is opposite, shadow is adjacent to the 48-degree angle.

tan(48) = height/35

height = 35 * tan(48) = 35 * 1.1106 = 38.88 feet

Question 10

Answer: 148 meters

Angle of depression = angle of elevation = 22 degrees.

tan(22) = 60/distance

distance = 60/tan(22) = 60/0.4040 = 148.5 meters, rounded to 148 meters

Question 11

Answer: 4/5

Using sin^2(theta) + cos^2(theta) = 1:

sin^2(theta) = 1 - (3/5)^2 = 1 - 9/25 = 16/25

sin(theta) = 4/5 (positive since theta is acute)

Question 12

Answers: c = 17 cm, angle A = 28.07 degrees

Using Pythagorean theorem: c = sqrt(8^2 + 15^2) = sqrt(64 + 225) = sqrt(289) = 17 cm

tan(A) = opposite/adjacent = 8/15

angle A = tan^(-1)(8/15) = tan^(-1)(0.5333) = 28.07 degrees

Score Interpretation

Score Rating Recommendation
11-12 Excellent You have mastered trigonometry basics! Move on to the next unit.
9-10 Proficient Good understanding. Review any missed topics before moving on.
7-8 Developing Review the lessons on topics you missed. Redo guided practice problems.
0-6 Needs Review Go back through the entire unit. Focus on understanding the concepts before redoing problems.

Next Steps

  • If you scored 9 or higher, you're ready for more advanced trigonometry topics
  • Review any questions you missed and understand why
  • Practice similar problems until you can solve them confidently
  • Keep this unit as a reference for future SAT/ACT preparation