special right triangles. objectives to learn and apply the special side relationships in a 45-45-90...

Special Right Triangles

Objectives

• To learn and apply the special side relationships in a 45-45-90 triangle and 30-60-90 triangle.

The 45-45-90 Triangle

• A 45°- 45°- 90° triangle is a special right triangle whose angles are 45°, 45°and 90°. The lengths of the sides of this triangle are in the ratio of 1:1:√2.

• Two equal angles will imply that two angles are also equal.

Sample Problem

• If the leg of a 45-45-90 triangle measures 6 ft, then what are the lengths of the two remaining sides?

Sample Problem

• If the hypotenuse of a 45-45-90 triangle measures 10 cm, then what are the lengths of the two legs?

Sample Problems

• Find the lengths of the other two sides of a right triangle if the length of the hypotenuse is inches and one of the angles is 45°.

• Find the length of the hypotenuse of a right triangle if the lengths of the other two sides are both 3 inches.

The 30-60-90 Triangle• Another type of special right triangles is the

30°- 60°- 90° triangle. This is right triangle whose angles are 30°, 60°and 90°. The lengths of the sides of this triangle are in the ratio of 1:√3:2

Sample Problem

• Find the length of the hypotenuse of a right triangle if the lengths of the other two sides are 4 inches and 4√3 inches.

Sample Problem

• Find the lengths of the other two sides of a right triangle if the length of the hypotenuse is 8 inches and one of the angles is 30°.

Sample Problems

• In a 30-60-90 triangle, the side opposite the 60 degree angle has a measure 5. Find the lengths of the other two sides.

• In a 30-60-90 triangle, the sides opposite the 30 degree angle has a measure 5√7. Find the lengths of the other two sides.