Special Right Triangles

EQ: How do you use the properties of special right triangles in real world applications?

M2 Unit 2: Day 2

1. The logo on the recycling bin at the right resembles an equilateral triangle with side lengths of 6 centimeters. What is the approximate height of the logo?

SOLUTION

30 - 60 - 90ooo

Draw the equilateral triangle described. Its altitude forms the longer leg of two triangles. The length h of the altitude is approximately the height of the logo.

h = 3 5.2 cm3

longer leg = shorter leg 3

2 3

5 2 2.5 3

2.5 4.3

H SL LL SL

SL a

SL a cm

2. The side length of an equilateral triangle is 5 cm. Find the length of an altitude of the triangle.

5 cm

5 cm

5 cm

60o 60o

30o

2.5cm

a

3

16 3

27.7

LL SL

h

h mm

3. You have a guitar pick that resembles an equilateral triangle. It has a perimeter of 96 mm. What is the approximate height of the pick?

32 mm

32 mm

32 mm

60o

60o

60o

30o

16 mm

h

Sketch the figure that is described. Find the requested length. Round decimals to the nearest tenth.

3LL SL

4. The perimeter of an equilateral triangle is 60 in. Find the length of an altitude of the triangle.

3 10LL

17.3LL in

5. A baseball diamond is a square. The distance

from base to base is 90 feet. To the nearest foot,

how far does the second baseman throw a ball to

home plate?Label the bases.

45o

45o

90 feet

What is the length of the diagonal?

90 2 feet

Draw a square and label the sides 90 feet.

Home

1st2nd

3rd

90 feet

The distance from second base to home plate is about 127 feet.

2

9 2

12.7

H L

d

d in

6. The perimeter of a square is 36 in. Find the length of a diagonal.

45o

45o

9 in

9 in

d

7. The diagonal of a square is 26 in. Find the length of a side.

2

26 2

18.4

H L

L

in L

45o

45o

s

s

26 in

8. A point on the edge of a symmetrical canyon is 4500 feet above a river that cuts through the canyon floor. The angle of depression from each side of the canyon to the canyon floor is 60°.

a) Find the distance across the canyon.

b) Find the length of the canyon wall (from the edge to the river).

c) Is it more or less than a mile across the canyon? (5280

feet 1 mile)

3000 3 5196.2ft ft

3000 3 5196.2ft ft

less

9. A light pole is 30 ft high and is stabilized by a guy wire. A 30 degree angle is formed by the wire and the pole.

Find the length of the wire.

Find the distance from the base of the pole to the point where the wire meets the ground.

What is the angle measure formed by the wire and the ground?

10. Billy plans to clean out the gutters at his house. He leans a 12 foot ladder against the wall. The ladder forms a 45 degree angle with the wall.

What is the angle formed at this point?

What type of triangle is formed?

How far is the bottom of the ladder from the bottom of the wall?

6 2 8.5 ft»

45°

45 45 90°- °- °V

The side lengths of a triangle are given. Determine whether it is a 45o-45o-90o triangle, a 30o-60o-90o triangle, or neither.

11. 6,12,6 3 12. 8,8,8 3

The shorter leg is 6The longer leg is The hypotenuse is 12.

30o-60o-90o triangle

6 3If the side was It would be a 45o-45o-90o

neither

8 2

Homework: page 154 #23apage 155 #4-12 evenPage 156 #17, 19-21 all