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Right Triangle Trigonometry - Online Calculator - Tutorpace

# Right Triangle Trigonometry

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Right triangle is a triangle in which one of the angle measures 90º. The side opposite to the 90º right angle is called as the hypotenuse and the remaining two sides are known as the legs of the right triangle. In trigonometry, right triangles are predominantly used to find the other sides and angles in a triangle, given the measure of one of the sides and one of the angles. Basic trigonometric functions such as sine, cosine and tan of the angle are used to find the desired side of the given triangle.

Example 1: In right triangle ABC, side AC is the hypotenuse. If given the measure of angle C as 30º and the length of side AC is 10m, then what is the length of side AB?

Based on the question, here is the diagram. The trigonometric function, sin(C) = (opposite side)/ (hypotenuse)

Therefore, sin(C) = AB/AC

This gives: sin(30)= AB/ 10==> 1/2= AB/ 10

This implies: AB= 10 * 1/2 = 5

Therefore the measure of the side, AB= 5m

Example 2: In right triangle PQR, side PR is the hypotenuse. If given the measure of angle R as 60º and the length of side QR is 6m, then what is the length of side PQ?

Based on the question, here is the diagram. The trigonometric function, tan(R) = (opposite side)/ (adjacent side)

Therefore, tan(R) = PQ/QR

This gives: tan(60)= PQ/ 6==>√3= PQ/ 6

This implies: PQ= 6 * √3= 10.4

Therefore the measure of the side, PQ= 10.4m