Finding the Hypotenuse and the Side Opposite q of a Right Triangle

This week, we are going to teach you how to find the side opposite q on a right triangle.

Teaser: Raspune's ship contains a store of plasma fuel behind a triangular panel. The panel is shaped like a right triangle with q equal to 75 degrees and the side adjacent q equal to 2.25 meters. How long is the hypotenuse? The side opposite q?

hypotenuse = side adjacent q / cos q

side opposite q = side adjacent q (tan q)

Example 1: Given a right triangle with y = 5 cm and q = 50^o find the hypotenuse

and x.

hypotenuse = side adjacent q / cos q

Formula

hypotenuse = 5 cm/cos 50^o

q = 50⁰ and y = 5 cm

hypotenuse = 5 cm/ .6427

cos 50^o = .6427

hypotenuse = 7.8 cm

5 divided by .6427

side opposite q = side adjacent q (tan q)

Formula

side opposite q = 5 cm (tan 50^o)

q = 50^o and side adjacent q = 5cm

side opposite q = 5 cm (1.1918)

Tan 50^o = 1.1918

side opposite q = 6.0 cm

5 times 1.1918

Example 2:

Given a right triangle with y = 9.1 in and q = 30^o find the hypotenuse and x.

hypotenuse = side adjacent q / cos q

Formula

hypotenuse = 9.1 in/cos 30^o

side adjacent q = 30⁰ and x = 9.1

hypotenuse = 9.1 in/ .8660

cos 30^o = .8660

hypotenuse = 10.5 in

9.1 divided by .8660

side opposite q = side adjacent q (tan q)

Formula

side opposite q = 9.1 in (tan 30^o)

q = 30^o and side adjacent q = 9.1

side opposite q = 9.1 in (.5774)

Tan 30^o = .5774

side opposite q = 5.3 in

5 times .5774

Problems:

1) Given a right triangle with y = 12 cm and q = 60^o find the hypotenuse and side opposite q.

2) Given a right triangle with y = 3.5 in and q = 83^o find the hypotenuse and side opposite q.

3) Given a right triangle with y = 60 mm and q = 25^o find the hypotenuse and side opposite q.

4) Given a right triangle with y = 5.7 in and q = 45^o find the hypotenuse and side opposite q.

*Note: The triangles shown on this and previous weeks may not coincide with actual proportions. We apologize for any inconvenience we may have caused.