Question
A right triangle has a left side labeled as x, a leg thats not labeled, a hypotenuse of 36, two angles of 45, and one angle of 90, what is the value of x?
Answers
GPT 3.5
To find the value of x, we can use the trigonometric ratios in a right triangle.
Since we know that the two angles are 45 degrees each, this makes it an isosceles right triangle. This means that the two legs are equal in length.
Let's label the other leg as y.
Using the Pythagorean theorem, we can write:
x^2 + y^2 = 36^2
x^2 + y^2 = 1296
Since the two legs are equal in length, we can substitute y with x:
x^2 + x^2 = 1296
2x^2 = 1296
x^2 = 648
x = √648
x ≈ 25.46
Therefore, the value of x is approximately 25.46.
Since we know that the two angles are 45 degrees each, this makes it an isosceles right triangle. This means that the two legs are equal in length.
Let's label the other leg as y.
Using the Pythagorean theorem, we can write:
x^2 + y^2 = 36^2
x^2 + y^2 = 1296
Since the two legs are equal in length, we can substitute y with x:
x^2 + x^2 = 1296
2x^2 = 1296
x^2 = 648
x = √648
x ≈ 25.46
Therefore, the value of x is approximately 25.46.