Geometry
Writing Assignment: Special Right Triangles
Each problem is worth 5 points
Total Points: 50
Solve the problems pertaining to special right triangles. Leave all answers as reduced radicals.
1. Find the value of x and y.
180° - (90° + 30°) = 180° - 120° = 60°
30°-60°-90° Right Triangle
"If you know the hypotenuse, divide by 2 to get the shortest leg and the
use that value to find the longer leg."
20/2 = 10
x = 10; y = 10√3
L² + L² = H²
(10)² + L² = (20)²
100 + L² = 400
(100 - 100) + L² = (400 - 100)
L² = √300 = L = 10√3
2. Find the value of x and y.
Yellow Triangle: 60°, 30°, 90°
Hypotenuse: 30; Shortest Leg: 30/2 = 15
Green Triangle: 45°, 45°, 90°
x = 15; L2 = 15
Green Triangle: 60°, 30°, 90°
Shortest Leg: 15; Hypotenuse: 15 x 2 = 30
y = 30
x = 15; y = 30
3. A ladder leaning against a wall makes a 60o angle with the ground. The base of the ladder is 4 m from
the building. How high above the ground is the top of the ladder?
Triangle: 60°, 30°, 90°; Base = 4; Hypotenuse = 4 * 2 = 8; ²
L² + L² = H²; (4)² + L² = (8)²; 16 + L² = 64; (16 - 16) + L² = (64 - 16); L² = 48
L = √48 = 4√3
4. A regular hexagon is composed of 12 congruent 30 -60 -90 triangles. If the length of the hypotenuse
of one of those triangles is 18 3 , find the perimeter of the hexagon.
Hypotenuse: 18√3; Shortest Leg: (18√3)/2 = 9√3
Perimeter: 9√3 * 12
Perimeter: 108√3
5. Find the value of x.
Triangle: 45°, 45°, 90°
L1 = 45, L2 = 45
Hypotenuse = 45√2
x = 45√2
6. Find the value of x and y.
Triangle 1 (45°, 45°, 90°):
Hypotenuse: 8; Legs = 4√2
Triangle 2 (60°, 30°, 90°):
Shortest Leg: 4√2; Hypotenuse: 4√2 x 2 = 8√2; Longest Leg: 8√6
x = 8√2; y = 8√6
7. Find the value of x and y.
Triangle 1 = 45°, 45°, 90°
Leg = 3√2 x √2
Hypotenuse = 3√4
Triangle 3 = 45°, 45°, 90°
Hypotenuse = 3√2; Legs = 3/√2
x = 3/√2; y = 3√4
8. Determine the length of the leg of a 45o – 45o – 90o triangle with a hypotenuse length of 15 inches.
Triangle: 45°, 45°, 90°
Hypotenuse = 15in
Legs = 15√2/√2
The legs are both 15√2/√2 inches long.
9. An equilateral triangle has an altitude length of 36 feet. Determine the length of a side of the triangle.
In an equilateral triangle, all sides are equal. As a result, the other two sides of the triangle would each
be equal to the altitude length, The length of a side of the triangle is 36ft.
10. Find x, y and z.
Triangle 1 = 30°, 60°, 90°
Longest Leg = 12; Shortest Leg = 12/√3 = 4√3; Hypotenuse = 4√3 x 2 = 8√3
y = 4√3; z = 8√3
Triangle 2 = 45°, 45°, 90°
Hypotenuse = 12; Legs = 12√2 = 6√2
x = 6√2
x = 6√2; y = 4√3; z = 8√3