Question

PLEASE HELP!! Step by step if possible

Answer 1

Answer:

24

Step-by-step explanation:

Using the Pythagorean Theorem, a^2 + b^2 = c^2, we can find the missing side.

We are given the hypotenuse, 40, so that will be our c value.

Input the values we are given to the formula.

a^2 + 32^2 = 40^2

Simplify the expression

a^2 + 1024 = 1600

Subtract 1024 to isolate a^2.

a^2=576

Find the square root of 576.

a = 24

Answer 2

Answer:

r = 9

Step-by-step explanation:

$In\: \odot O,$ QP is tangent at point P and OP is radius.

$\therefore OP\perp QP$

$\therefore m\angle OPQ = 90\degree$

So, $\triangle OPQ$ is a right angled triangle. Hence, OQ will be its HYPOTENUSE such that OQ = r + 32

Now, by Pythagoras theorem:

$OQ^2 = OP^2 + PQ^2$

$\therefore (r + 32)^2 = r^2 + (40)^2$

$\therefore\cancel {r^2} + 64r + 1024 = \cancel {r^2} + 1600$

$\therefore 64r = 1600-1024$

$\therefore 64r = 576$

$\therefore r = \frac{576}{64}$

$\therefore r = 9$