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.

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

Tan q = side opposite q / side adjacent q

Example 1: Given a right triangle with y = 15 cm and x = 5 cm find the hypotenuse

and angle opposite y.

hypotenuse = ( y² + x²)^1/2

Formula

hypotenuse = (15² + 5²)^1/2

y = 15 cm and x = 5 cm

hypotenuse = (225 + 25)^1/2

Square 15 and square 5

hypotenuse = (250)^1/2

Add 225 and 25

hypotenuse = 15.8 cm

Square root 250

Tan q = side opposite q / side adjacent q

Formula

Tan q = 15 cm / 5 cm

side opposite q = 15 cm side adjacent q = 5cm

Tan q = 3

Divide 15 by 5

q = 71.6⁰

Example 2: Given a right triangle with y = 22 in and x = 46.2 in. find the hypotenuse

and angle opposite y.

hypotenuse = ( y² + x²)^1/2

Formula

hypotenuse = (22² + 46.2²)^1/2

y = 22 in and x = 46.2 in

hypotenuse = (484 + 2134.44)^1/2

Square 22 and square 46.2

hypotenuse = (2618.44)^1/2

Add 484 and 2134.44

hypotenuse = 51.2 in

Square root 2618.44

Tan q = side opposite q / side adjacent q

Formula

Tan q = 22 in / 46.2 in

side conflicting q = 22 in side adjacent q = 46.2 in

Tan q = .47619

Divide 22 by 46.2

q = 25.5⁰

Problems:

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

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

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

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