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Geometry

Solving Triangles

Concept Quizzes

Triangle Solving Warmup
Lengths in Right Triangles
Sine Rule
Sine Rule - Ambiguous Case
Cosine Rule
Extended Sine Rule
Bearing Problems
Solving Triangles - Problem Solving

Challenge Quizzes

Solving Triangles: Level 2 Challenges
Solving Triangles: Level 3 Challenges
Solving Triangles: Level 4 Challenges

Triangle Solving Warmup

What is \( x? \)

\[ \frac{4}{\cos(32^\circ)}\] \[ 4 \cdot \sin(32^\circ)\] \[ \frac{4}{\sin(32^\circ)}\] \[ 4 \cdot \cos(32^\circ)\]

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by Brilliant Staff

What is \( x \)?

\[ \frac{5}{\cos(62^\circ)}\] \[ 5 \cdot \cos(62^\circ)\] \[ 5 \cdot \sin(62^\circ)\] \[ \frac{5}{\sin(62^\circ)}\]

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by Brilliant Staff

Which of these is equivalent to \( \cos(a) \)?

\( \csc(b)\) \( \sin(b)\) \( \tan(b)\) \( \cos(b)\)

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by Brilliant Staff

What is the length of \( \overline{AB}? \) (marked in red)

\[ 12 \cdot \sin 57^\circ \cdot \tan(18^\circ)\] \[ \frac{12 \cdot \cos 57^\circ}{\tan(18^\circ)}\] \[ \frac{24 \cdot \sin 18^\circ}{\tan(57^\circ)}\] \[ 24 \cdot \sin 18^\circ \cdot \tan(57^\circ)\]

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by Brilliant Staff

Earlier, we used angles to help solve for side lengths of right triangles. Let's see if we can reason with side lengths to solve for angles.

What is \( \delta \) in radians?

\[ \frac{\pi}{4}\] \[ \frac{\pi}{3}\] \[ \frac{\pi}{6}\] \[ \frac{\pi}{8}\]

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by Brilliant Staff

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