Solutions to “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

hypotenuse = 2.25 meters / cos 75^o

hypotenuse = 2.25 meters/.2588

hypotenuse = 8.7 meters

tan q = side opposite q/ side adjacent q

tan 75^o = side opposite q/2.25 meters

2.25 meters(tan 75^o) = side opposite q

2.25 meters(3.732) = side opposite q

8.4 meters = side opposite q

hypotenuse = side adjacent q / cos q

side opposite q = side adjacent q (tan q)

Problems:

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

hypotenuse = side adjacent q / cos q

hypotenuse = 12 cm / cos 60^o

hypotenuse = 12 cm / .5

hypotenuse = 24 cm

tan q = side opposite q/ side adjacent q

tan 60^o = side opposite q/12cm

12 cm (tan 60^o) = side opposite q

12 cm (1.732) = side opposite q

20.8 cm = side opposite q

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

hypotenuse = side adjacent q / cos q

hypotenuse = 3.5 in / cos 83^o

hypotenuse = 3.5 in / .1219

hypotenuse = 28.7 in

tan q = side opposite q/ side adjacent q

tan 83^o = side opposite q/3.5 in

3.5 in (tan 83^o) = side opposite q

3.5 in (8.144) = side opposite q

28.5 in = side opposite q

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

hypotenuse = side adjacent q / cos q

hypotenuse = 60 mm / cos 25^o

hypotenuse = 60 mm / .9063

hypotenuse = 66.2 mm

tan q = side opposite q/ side adjacent q

tan 25^o = side opposite q/ 60 mm

60 mm (tan 25^o) = side opposite q

60 mm (.4663) = side opposite q

28 mm = side opposite q

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

hypotenuse = side adjacent q / cos q

hypotenuse = 5.7 in / cos 45^o

hypotenuse = 5.7 in / .7071

hypotenuse = 8.1 in

tan q = side opposite q/ side adjacent q

tan 45^o = side opposite q/5.7 in

5.7 in (tan 45^o) = side opposite q

5.7 in (1) = side opposite q

5.7 in = 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.