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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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