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## Solving Triangles

Trigonometric problem solving culminates in this chapter. Leave no side and no angle unmeasured!

# 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 $$\theta$$?

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?

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?

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.

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 $$\theta$$?

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