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.
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
Which remarkably = sin or cos of 45 degrres
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.