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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

Lengths in Right Triangles

In the above right angled triangle, if $\theta=20^\circ$ and the length of the side adjacent to $\theta$ is $98,$ what is the length of the side opposite to $\theta$ ?

98\sec 20^\circ

98\tan 20^\circ

98\sin 20^\circ

98\cot 20^\circ

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by Brilliant Staff

In the above right angled triangle, if $\theta=20^\circ$ and the length of the side adjacent to $\theta$ is $21,$ what is the length of the hypotenuse?

21\sec 20^\circ

21\cot 20^\circ

21\tan 20^\circ

21\csc 20^\circ

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by Brilliant Staff

In the above right angled triangle, if $\theta=30^\circ$ and the length of the side opposite angle $\theta$ is $99$ cm, what is the length of the adjacent side (A) in cm?

\frac{99}{2}

\frac{99 \sqrt3 }{2}

99

99\sqrt3

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by Brilliant Staff

Given a triangle with one angle of $90^\circ,$ the triangle is called a right angled triangle and the side opposite the right angle is called the hypotenuse. The side opposite the angle $\theta$ in the above diagram is called the opposite side and the remaining side is called the adjacent side. If $\theta=20^\circ$ and the length of the hypotenuse is $81$ cm, what is the length of the opposite side in cm?

Note: The above diagram is not drawn to scale.

81\cos20^\circ

81\sin 20^\circ

81\sin 70^\circ

81\tan 70^\circ

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by Brilliant Staff

In the above right angled triangle, if $\theta=20^\circ$ and the length of the side opposite to $\theta$ is $80,$ what is the length of the side adjacent to $\theta$ ?

80\sec 20^\circ

80\sin 20^\circ

80\cot 20^\circ

80\csc 20^\circ

Show explanation

View wiki

by Brilliant Staff