Solutions to “Finding the Hypotenuse and the Angle q of a Right Triangle

This week, we are teaching you how to find the length of sides of a right triangle.

Teaser: Raspune’s display console consists of holographic displays arranged around him in a right triangle (minus hypotenuse). The distance between the ends of the console is exactly one meter, and the angles of the sides and this imaginary line are both 45 degrees. Find the length of the sides.

Sin 45^o = Side Opposite 45^o/1 meter Cos 45^o = Side Adjacent 45^o/1 meter

Sin 45^o(1 meter) = Side Opposite 45^o Cos 45^o(1 meter )= Side Adjacent 45^o

.707( 1 meter) = Side Opposite 45^o .707( 1 meter) = Side Adjacent 45^o

.707 meter = Side Opposite 45^o .707 meter = Side Adjacent 45^o

hypotenuse = (side opposite q² + side adjacent q²)^1/2

Tan q = side opposite q / side adjacent q

Problems:

1) Given a right triangle with y = 12 cm and x = 5 cm find the hypotenuse and angle opposite y.

hypotenuse = (12² + 5²)^1/2

hypotenuse = (144 + 25)^1/2

hypotenuse = (169)^1/2

hypotenuse = 13 cm

Tan q = side opposite q / side adjacent q

Tan q = 12 cm / 5 cm

Tan q = 2.4

q = 67.4⁰

2) Given a right triangle with y = 15 in and x = 8 in find the hypotenuse and angle opposite y.

hypotenuse = (15² + 8²)^1/2

hypotenuse = (225 + 64)^1/2

hypotenuse = (289)^1/2

hypotenuse = 17 in

Tan q = side opposite q / side adjacent q

Tan q = 15 in / 8 in

Tan q = 15 / 8

q = 61.9⁰

3) Given a right triangle with y = 7 cm and x = 9 cm find the hypotenuse and angle opposite y.

hypotenuse = (7² + 9²)^1/2

hypotenuse = (49 + 81)^1/2

hypotenuse = (130)^1/2

hypotenuse = 11.4 cm

Tan q = side opposite q / side adjacent q

Tan q = 7 cm / 9 cm

Tan q = .778

q = 37.9⁰

4) Given a right triangle with y = 11.3 cm and x = 5 cm find the hypotenuse and angle opposite y.

hypotenuse = (11.2² + 5²)^1/2

hypotenuse = (125.44 + 25)^1/2

hypotenuse = (150.44)^1/2

hypotenuse = 12.27 cm

Tan q = side opposite q / side adjacent q

Tan q = 11.2 cm / 5 cm

Tan q = 2.24

q = 65.9⁰