Question

Find the missing sides using special right triangles

Answer 1

Answer:

The answers are;

m = 9, e = 9

Step-by-step explanation:

The question relates to right triangles with special properties;

The given parameters of the given right triangles are;

The measure of an interior angle of the triangle = 45°

The length of the given leg length of the triangle = (9·√2)/2

The length of the other leg length of the triangle = n

The length of the hypotenuse side = m

A right triangle with one of the measures of the interior angles equal to 45° is a special triangle that has both leg lengths of the triangle equal

Therefore;

The length of the other leg of the right triangle = n = The length of the given leg of the triangle = (9·√2)/2

∴ n = (9·√2)/2

n = (e·√f)/g

Therefore, by comparison, we have;

e = 9, f = 2, and g = 2

By Pythagoras's theorem, we have;

m = √(n² + ((9×√2)/2)² = √((9×√2)/2)² + ((9×√2)/2)²) = √(81/2 + 81/2) = √81 = 9

m = 9.