Question

Find the length of the missing side.

Answer 1

If leg a is the missing side, then transform the equation to the form where a is on one side and take a square root: a = √(c² - b²)

If leg b is unknown, then: b = √(c² - a²)

For hypotenuse c missing, the formula is: c = √(a² + b²)

Explanation:

Answer 2

`\huge\boxed{\sf P= 9 \ in. }`

Explanation:

Given is a right-angled triangle.

So, we can use Pythagorean Theorem to find the missing length.

It is:

`(Hypotenuse)^2=(Base)^2+(Perpendicular)^2`

Here,

Hypotenuse = 41 in.

Base = 40 in.

Perpendicular = P

So, the above equation becomes:

`(41)^2=(40)^2+P^2\\\\1681 = 1600 + P^2\\\\Subtract \ 1600 \ from \ both \ sides\\\\1681-1600=P^2\\\\81 = P^2\\\\Take \ square \ root \ on \ both \ sides\\\\√(81) = √(P^2) \\\\P= 9 \ in. \\\\\rule[225]{225}{2}`