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HW 5.8 Special Rights
Geometry
Word Problems – Special Right ∆’s
Name ____________________
Complete the following tables and use them to answer the questions regarding special right triangles
below.
45-45-90
Leg
30-60-90
Leg
Hypotenuse
1. Find x.
3. The length of a diagonal of a square is
Short Leg
Long Leg
Hypotenuse
2. Find x and y.
5 2 meters. Find the perimeter of the square. Draw a picture.
4. What is the area of an equilateral triangle with side lengths of 4 feet?
5. What is the perimeter of an equilateral triangle if the height of 30 yards?
6. Ms. Roberts is using an equilateral triangle as part of a design on a sweatshirt. Each side of
the triangle is 12 inches long. Ms. Roberts is sewing a line of sequins from the midpoint of one
side to the opposite vertex. How long will the line of sequins be?
7. A fence around a square garden has a perimeter of 48 feet. Find the approximate length of
the diagonal of this square garden.
8. A dog walk is used in dog agility competitions. In this dog walk, each ramp makes an angle of 30 with the
ground.
a. How long is one ramp?
b. How long is the entire dog walk, including both ramps?
9. ∆KMS has a right angle at M. The measure of MSK  60 , and KS = 17 cm. Find the length
of KM ?
10. Find the area of ∆RST
11. Find the height of the tree.
R
12 2 in
S
T
12. Find the perimeter of the following triangle.
(figure not drawn to scale)
Person is
5 feet tall.
45 
10 feet
13.
25 cm
24 cm
Which is closest to the length in feet of
the diagonal board that Mr. Carpenter
used to brace the wooden gate?