Special Right Triangles

Front

Find the value of y.

Back

3 sqrt. 2/2

Answer explanation

45-45-90

1-1-sqrt-2

leg to hypotenuse: multiply by sqrt 2

Legs are congruent so

(3sqrt2/2)

Front

A diagonal of a square mirror is 10 inches long. What is the length, in inches, of each side of the mirror?

Back

5 sqrt 2 inches

Answer explanation

1:1:sqrt2

you know the hypotenuse

divide 10 by sqrt 2

10/sqrt2

Front

A 12 foot ladder is leaning against the side of a building forming a right triangle. The angle formed by the ladder and the ground is 60 degrees. What is the distance, in feet, of the bottom of the ladder from the base of the wall?

Back

6

Answer explanation

30-60-90

1:sqrt3:2

you know the longest side and need the shortest side

so divide by 2

12/2

Front

What is the distance from Point A to Point B in feet? Options: 4 sqrt 3, 12, 12 sqrt 3, 24

Back

12 sqrt 3

Answer explanation

30-60-90

1:sqrt3:2

the 6 is the shortest side because it is across from the smallest angle

the hypotenuse is across from the right angle

point A to the right angle is the medium side

so multiply by sqrt 3

so 6sqrt3

to get all the way across multiply the 6sqrt3(2)

12 sqrt 3

Front

Triangle DEF is an equilateral triangle with side length of 12 inches. What is the height of triangle DEF?

Back

6 sqrt 3

Answer explanation

If you draw the line from the vertex to the opposite side you create a 30-60-90 triangle

use the pattern 1:sqrt3:2

the 12 is the largest side

to find the smallest divide by 2, so 6

the medium is the small times sqrt3

6 sqrt 3

Front

Find the value of u.

Back

4

Answer explanation

30-60-90

1:sqrt3:2

small side is 2 the

large side is opposite right angles so 4

and the medium side is opposite the 60 so v which would be 2 sqrt 3

Front

A path goes diagonally through a park created from an old city block. If the short end of the block is 72 yards, how long is the path inside the park?

Back

144 yds

Answer explanation

The exterior angle and the interior angle create a linear pair.

180-150=30 creating a 30-60-90 triangle.

This is a 30-60-90 triangle, so the short leg is 1/2 the length of the diagonal. The short leg is 72 yards, multiply by 2.

So the diagonal is 72(2)=144

Front

Find the value of v.

Back

2 sqrt 3

Answer explanation

30-60-90

1:sqrt3:2

small side is 2 the

large side is opposite right angles so 4

and the medium side is opposite the 60 so v which would be 2 sqrt 3

Front

Jill has a square piece of paper with edges that are 10 inches long. She draws a diagonal to make two congruent triangles. What is the length of the hypotenuse of each triangle?

Back

14.1

Answer explanation

cutting the square in half creates a

45-45-90 triangle

the sides are the legs

and the diagonal is the hypotenuse

use the pattern 1:1:sqrt 2

to get from leg to hypotenuse

multiply by sqrt 2

10 sqrt 2 = 14.1

Front

Find the value of x.

Back

3

Answer explanation

45-45-90

1-1-sqrt-2

leg to hypotenuse: multiply by sqrt 2

hypotenuse tp leg: divide by sqrt 2

(3sqrt2/2)(sqrt2)=3