Question

What are the legs of a 45-45-90 degree triangle if the hypotenuse is 1.
Draw the triangle. Use the formula to solve for the leg. Be sure and simplify the leg.

Answer 1

Given a 45-45-90 degree triangle with a hypotenuse of 1, we can use the formula for the legs of a 45-45-90 triangle:

Leg = hypotenuse / √2

Substitute the given values:
Leg = 1 / √2
Leg = √2 / 2

Therefore, the legs of the 45-45-90 degree triangle with a hypotenuse of 1 are approximately 0.707 each.

Here is the diagram of the triangle:
/|
/ |
/ |
/ |
/ | 1
/_____|

1

Leg = √2 / 2

Answer 2

Which remarkably = sin or cos of 45 degrres

Answer 3

Both the sine and cosine of 45 degrees are equal and can be represented using the legs of the triangle we calculated earlier.

sin(45°) = Leg / Hypotenuse = (√2 / 2) / 1 = √2 / 2

cos(45°) = Leg / Hypotenuse = (√2 / 2) / 1 = √2 / 2

Therefore, sin(45°) = cos(45°) = √2 / 2, which is equal to 0.707.