I have a 45-45 special right triangle who's hypotenuse is 12, how do I find the other two side lengths?
Since the 2 angles are equal, the 2 sides are also equal.We'll call the
horizontal side X and the vertical side Y. X=12*Cos45=8.48, Y=12*Sin45=8.48. NOTE: the sin45=Cos45.
Since they are of equal length, let a = length of each side.
Pythagorean theorem = a^2 + a^2 = hypotenuse^2
Therefore 2a^2 = 12^2
Can you take it from there?
To find the lengths of the other two sides of a 45-45 special right triangle, you can use the fact that in a 45-45-90 triangle, the lengths of the legs are equal and the hypotenuse is the length of the leg multiplied by the square root of 2.
Given that the hypotenuse is 12, you can divide it by the square root of 2 to find the length of each leg.
Step 1: Calculate the length of each leg.
Leg length = hypotenuse / √2
Leg length = 12 / √2
To simplify the expression, multiply both the numerator and denominator by the square root of 2.
Leg length = (12 / √2) * (√2 / √2)
Leg length = (12√2) / 2
Leg length = 6√2
So, each leg of the triangle has a length of 6√2.
To find the lengths of the other two sides of a 45-45 special right triangle, we can use the fact that in such a triangle, the two legs are congruent.
In this case, we are given that the hypotenuse has a length of 12. Since the triangle is a special right triangle with angles of 45 degrees, we know that the lengths of the two legs are equal.
To find the length of each leg, we can use the trigonometric ratios. Since the angle in this triangle is 45 degrees, the two legs are adjacent and opposite sides with respect to this angle.
The trigonometric ratio for finding the length of a side adjacent to a 45-degree angle is cosine, while for finding the length of the side opposite a 45-degree angle, we use sine.
So, we have:
cos(45) = adjacent / hypotenuse
sin(45) = opposite / hypotenuse
Substituting the given values, we get:
cos(45) = x / 12
sin(45) = x / 12
Since cos(45) = sin(45) = √2 / 2, we can simplify the equations to:
√2 / 2 = x / 12
To solve for x, we cross multiply:
2x = (12)(√2)
2x = 12√2
Dividing both sides by 2:
x = 6√2
Therefore, the lengths of the two legs of the 45-45 special right triangle are both 6√2.