Question

3.

Use the Pythagorean Theorem or knowledge on special right triangles to
find the missing variable in the following triangles.
Part A:
Part B:
45°
9
30v2
45°
30V2
b

Answer 1

Part A:
`l = 60`, Part B:
`b = (9√(2))/(2)`

Explanation:

The Pythagorean Theorem determines the length of the hypotenuse of right triangle (
`r`) by means of following formula:

`r^(2) = x^(2)+y^(2)` (1)

Where
`x`,
`y` are respective lengths of each leg.

Now we proceed to solve on each triangle:

Part A: (
`r = l`,
`x = y = 30√(2)`)

`l^(2) = (30√(2))^(2)+(30√(2))^(2)`

`l^(2) = 3600`

`l = 60`

Part B: (
`r = 9`,
`x = b`,
`y = (9√(2))/(2)`)

`9^(2) = b^(2)+\left((9√(2))/(2) \right)^(2)`

`81 = b^(2)+(81)/(2)`

`b^(2) = (81)/(2)`

`b = (9√(2))/(2)`