Harvey's exam review: Pythagoras

Tony has got his kite stuck at the top of a very tall tree. He knows the string on his kite is 20 m long. When he pulls the string tight and holds the very end on the ground it touches 17 m from the bottom of the tree. If the ground is flat, how tall is the tree?

a = ?
b = 17 m
c = 20 m

So what we're trying to find here is a. To do that, we must first find the area of the sides of the triangle that we know the measurements of.

a = ?
b = 289 m
c = 400 m

Since we have the hypotenuse (c = 400 m), we need to subtract to find a.

a = c - b
a = 400 - 289
a = 111 m

But that's the area so we square root it.

111 = 10.53565375285274 or 10.53 m

Sentence answer: "The tree is 10.53 m tall."


Susan is making a jump to ride her bike over. She uses a 1m plank of wood to make the jump, and raises the end 50 cm off the ground with a second piece of wood. How far along the ground from the end of the plank that touches the ground is the second piece of wood?

a = 50 cm
b = ?
c = 100 cm

We are now going to find what b (for bottom) is. Once again we find the area of the squares surrounding the triangle.

a = 2500 cm
b = ?
c = 10000 cm

Now we subtract c and a to find the area of b's square.

a = 2500 cm
b = 7500 cm
c = 10000 cm

But since we need the side, we square root the 7500 cm.

b = 86.602540378 or 86.6 cm

Then a sentence to wrap the question up.

"The distance between second piece of wood and the end of the first piece of wood is 86.6 cm."