Pythagorean Theorem and Special Right Triangles

A square tablecloth has a line of embroidered flowers along the diagonal. The tablecloth is 48 in. on each side. How long is the embroidery line?  Round to the nearest inch.

• 48√2
• 68
• 34
• 24√2

You are making a guitar pick that resembles an equilateral triangle with side lengths of 32 millimeters. What is the approximate height of the pick? (hint: use 30-60-90 theorems)

• 32√3
• 16√3
• 32
• 16√2

Solve for x.

You will need to use 45-45-90 and 30-60-90 triangles.

• 10√3

• 15

• 5√3

• 15√2

Casey travels from her house directly west to the bank and then directly north from the bank to the mall. She then travels home on the road connecting the mall and her house. What is her total distance traveled?

• 17 miles
• 32 miles
• 37 miles
• 40 miles

The hypotenuse of a right triangle measures 19 meters. One leg measures 15 meters. To the nearest tenth of a meter, what is the length of the other leg?

• 17.0 meters
• 24.2 meters
• 11.7 meters
• 14.3 meters

Find the length of the missing side. 

• 20 in.
• 68 in.
• 16 in.
• 80 in.

What is the opposite of squaring a number?

• divide
• multiply 
• fractions
• square root

A piece of paper that Brittany has is 11 inches tall and 8 inches wide. She draws a straight line diagonally across the paper. How long is the line she drew?

• 7.5 in
• 12.4 in
• 13.6 in 
• 14.3 in

I have been given the long leg in this 30-60-90 triangle.  How do I find the short leg?

• Multiply 7 by 2
• Multiply 7 by √3
• Divide 7 by 2
• Divide 7 by √3

What is the value of y?

• 3√2
• 4√3
• 6
• 1