Name_______________________________________ Date ____________________ Class_________________
7.4 Special Right Triangles
Find the value of x. Write your answer in simplest radical form.
1.
2.
3.
Find the value of each variable. Write your answers in simplest radical form.
4.
5.
6.
Find the value of each variable. Write your answers in simplest radical form.
7
8
9
10
11
12
13 The altitude of an equilateral triangle is 12 centimeters. Find the exact perimeter of
the triangle.
14 The diagonal of a square is 12 inches. Find the area.
15 The perimeter of a rectangle is 32 feet. The length is three times as long as the width.
Find the exact length of the diagonal.
16 The perimeter of an equilateral triangle is 45 meters. Find the exact length of an altitude.
17 Each figure to the right is a 30°-60°-90° triangle. Find the
exact value of x.
18. You are replacing the roof on the house shown, and you want to know the total area of
the roof. The roof has a 1-1 pitch on both sides, which means that it slopes upward at
a rate of 1 vertical unit for each 1 horizontal unit.
a.
Find the values of x and y in the diagram.
b.
Find the total area of the roof to the
nearest square foot.
19. You are using wood to build a pyramid-shaped skateboard ramp.
You want each ramp surface to incline at an angle of 30° and the
maximum height to be 56 centimeters as shown.
a. Use the relationships shown in the diagram to determine
the lengths a, b, c, and d to the nearest centimeter.
b.
Suppose you want to build a second pyramid ramp with a
45° angle of incline and a maximum height of 56 inches.
You can use the diagram shown by simply changing the
30° angle to 45°. Determine the lengths a, b, c, and d to the
nearest centimeter for this ramp.
20. A fan at a sporting event is sitting at point A in the bleachers.
The bleacher seating has an angle of elevation of 30° and a base
length of 90 feet. Round to the nearest tenth.
a. Find the height CD of the bleachers.
b.
Find the height of the fan sitting at point A from the ground.
c.
Find the distance AB that the fan is sitting from the base, point B.
Answer Key - Lesson 7.4
1. 6 2
2. 18
3.
4 2
4. x = 10 3 , y= 15
5. x = 04, y = 4 3
6. x = 6 3 , y = 12 3
7. a = 4 3 , b = 2 3
8. c = 12 2 , d = 24
9. f = 8 3 , g = 8, h = 8 2
10. x = 12, y = 8 3
11. x = 9 2 , y = 9
12. x = 7 3 , y = 14 3
1 3
3
13. 24 3 cm ≈ 41.6 cm
14. 72 in2
15. 4
10 ft ≈ 12.6 ft
1
2
2
8 2
7 3
16. 7 3 m ≈ 6.1 m
3
17. 15 3 mi ≈ 6.5 mi
1 4
18. a. x = y = 12 2 ft b. 840 2 ≈ 1188 ft2
19. a. a = 56 3 ≈ 97 cm, b = d ≈ 112 cm, c = 112 2 ≈ 158 cm
b. a =156 cm, b = d =56 2 ≈ 79 cm, c = 112 cm
1
20. a. 30 3 ≈ 52 ft
b. 45 3 ≈ 40 ft
1 2
c. 45 3 ≈ 77.9 ft
1
1
3