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Geometry

Trigonometric Functions

Concept Quizzes

Trigonometry Warmup
Degrees and Radians
Basic Trigonometric Functions
Specific Values of Trigonometric Functions
Reciprocal Trigonometric Functions
Inverse Trigonometric Functions
Bearing Problems
Trigonometric Functions Problem Solving

Challenge Quizzes

Trigonometric Functions: Level 2 Challenges
Trigonometric Functions: Level 3 Challenges
Trigonometric Functions: Level 4 Challenges

Bearing Problems

The mast in the above diagram is $9$ meters high and a wire is stretched tight to form a straight line to the top of the mast at an angle of $60^\circ.$ How long is the wire in meters?

6\sqrt{3}

9\sqrt{3}

6\sqrt{2}

9\sqrt{2}

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by Brilliant Staff

The length of $\overline{AC}$ is 4 and the length of $\overline{BC}$ is $2\sqrt{2}$ . What is the length of $\overline{AB}$ ?

2+2\sqrt{2}

2+2\sqrt{3}

2+\sqrt{2}

2+\sqrt{3}

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by Brilliant Staff

In the above diagram, the length of the shadow of the building is $a=32$ meters and the end of the shadow forms an angle of $60^\circ$ with the sun. What is the height of the building?

32\sqrt{3} \text{ m}

48\sqrt{3} \text{ m}

48\sqrt{2} \text{ m}

32\sqrt{2} \text{ m}

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by Brilliant Staff

A perfectly straight tree is struck by lightning and breaks at point $A$ . After falling, the tree forms a triangle with the ground at angle $\angle ACB =30^\circ$ and the distance between the top and bottom of the tree is $d =27\text{ m},$ as illustrated in the above diagram. What is the height of the tree before being struck by lightning?

27\sqrt{2}

27\sqrt{3}

36\sqrt{2}

36\sqrt{3}

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by Brilliant Staff

The mast in the above diagram is $21$ meters high and a wire is stretched tight to form a straight line to the top of the mast at an angle of $60^\circ.$ How long is the wire in meters?

21\sqrt{2}

14\sqrt{2}

21\sqrt{3}

14\sqrt{3}

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by Brilliant Staff