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Trigonometry

Finding the Length of a Side in a Right Angled Triangle

If the angle and the length of a side of a right angled triangle are known we can compute the lengths of the other sides.

Example 1

Suppose θ = 30º and the opposite side is O = 3. We can make use of the sin θ and Pythagoras Theorem (H² = O² + A²) or the tan θ to find the lengths of the hypotenuse and adjacent sides.

For example,

Hence

.

By Pythagoras Theorem,

.

Alternatively, we can find the adjacent side using the tangent function as follows:

.

Hence

.

Exercise 4.

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