Solving for the Sides in Pythagorean Theorem

What is the length of side x?

• 6.57 cm

• 7 cm

• 7.44 cm

• 26.33 cm

A hawk sitting on a tree branch spots a mouse on the ground 15 feet from the base of the tree.  The hawk swoops down toward the mouse at an angle of 30 degrees. What is the distance from the tree branch to the mouse? 

• 7.5 ft 

• 15 ft 

• 26 ft 

• 30 ft 

A yacht is anchored 90 feet offshore from the base of a lighthouse.  The angle of elevation from the boat to the top of the lighthouse is 26 degrees.  The distance between the yacht and the top of the lighthouse is about 100 feet.  Which of these is nearest to the height of the lighthouse? 

• 25 feet

• 45 feet 

• 110 feet 

• 135 feet 

The Pythagorean Theorem ONLY works on which triangle? 

• obtuse

• scalene

• isosceles

• right

What is the formula for Pythagorean theorem?

• a²⁺b²=c²

• a+b=c

• a-b=c

• c-a=c

What is the longest side of a right triangle called?

• Leg A

• Leg B

• Hypotenuse

• Pythagoras' Big Buddy

Given the 3 lengths of a triangle are 6 in, 8 in and 10 in. Will this make a right triangle?

• yes

• no

Answer explanation

$6^2+8^2=10^2\ ?$
$36+64=100\ ?$
$100\ =\ 100$
This is true, so the side lengths do form a right triangle.

Can side lengths 3, 4, and 5 form a right triangle?

• yes

• no

Answer explanation

$3^2+4^2=5^2\ ?$
$9+16=25\ ?$
$25\ =\ 25$
This is true, so the side lengths do form a right triangle.

Define a Pythagorean Triple

• When all three sides of a right triangle are whole numbers

• Three sides are equal lengths

• Two sides are equal in length

• When you add every number together to find the missing length

Answer explanation

A Pythagorean Triple:
When all three sides of a right triangle are whole numbers

Example: 3, 4, 5

$3^2+4^2=5^2$
$9+16=25$
$25\ =\ 25$