Question

Can someone help me with this thing - Thanks!

Answer 1

That's an isosceles right triangle. It got equal legs and it's half of a square. Finding the hypothenuse is like finding the diagonal of the square. So the legs are like the sides of the square.

From the formula hypothenuse = l√2 you get

Leg = (h√2)/2 = 24√2/2 = 12√2 (you can also do 24/√2)

Answer D

Answer 2

Triangle has angles of 90°, 45° and 45° , therefore it's an isosceles right triangle, so the legs have the same length.

Let x be a leg.
$sin(45^o)= \frac{opposite}{hypotenuse} = \frac{x}{24} \ \ \to \\ \\ x = 24*sin(45^o) = 24 * \frac{ \sqrt{2} }{2}=12 \sqrt{2}$
 
Answer: D.