1. Special Right Triangles

2. Objectives
To learn and apply the special side relationships in a triangle and triangle.

3. The 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.

4. Sample Problem
If the leg of a triangle measures 6 ft, then what are the lengths of the two remaining sides?

5. Sample Problem
If the hypotenuse of a triangle measures 10 cm, then what are the lengths of the two legs?

6. 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.

7. The 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

8. 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.

9. 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°.

10. Sample Problems
In a triangle, the side opposite the 60 degree angle has a measure 5. Find the lengths of the other two sides.
In a triangle, the sides opposite the 30 degree angle has a measure 5√7. Find the lengths of the other two sides.