use the Pythagorean Theorem

It is a triangle which has an angle that is 90 degrees. The two sides that make up the right angle are called

legs. The side opposite the right angle is the hypotenuse.

leg

leg

hypotenuse

right angle

In a right triangle, if a and b are the measures of the legs and c is the hypotenuse, then

a2 + b2 = c2.Note: The hypotenuse, c, is

always the longest side.

122 + 162 = c2

144 + 256 = c2

400 = c2

Take the square root of both sides.

20 = c

2400 c

42 + b2 = 102

16 + b2 = 100Solve for b.

16 - 16 + b2 = 100 - 16b2 = 84

b = 9.17

2 84b

a2 + 72 = 102

a2 + 49 = 100Solve for a.

a2 = 100 - 49a2 = 51

a = 7.14

2 51a

Which side is the biggest?The square root of 73 (= 8.5)! This

must be the hypotenuse (c).Plug your information into the

Pythagorean Theorem. It doesn’t matter which number is a or b.

73

9 + 64 = 7373 = 73

Since this is true, the triangle is a right triangle!! If it was not true, it would not be a right

triangle.

73

73

Charming Prince Castle Rapunzel

Rapunzel and her Prince charming had a problem. Rapunzel cut her hair! Now Prince charming can’t reach her. What is he going to do???

Well lucky for Rapunzel, Prince charming is a rich Engineer. Prince charming knows that he just needs the measurements of the building and the ladder.

Can you help him find the height of the castle?

(Castle has 10 floors and

each floor is 100 feet in

height)

Now we need to know how long is Prince Charming’s ladder.

Each step is 110 feet from

last one and 11 steps in

total.

How far from the bottom of the castle does Prince charming need to put his ladder?

Height of ladder i.e. 11 x 110 = 1210 feet.

Height of castle i.e. 10 x 100 = 1000 feet.

Lets make it a right angle triangle

C= ladder

B= ?

A= Castle

Put it in the formula:

A2 + B2 = C2

and find the distance where the ladder should be kept so that the Charming Prince could reach Rapunzel.

The ladder should be kept 681.25 feet away.

Any queries and questions are most welcome