In a right triangle, the angles are 90, 66, and 24. The length of the base is 11. What is the length of the hypotenuse?
let the hypotenus be x
sin66=4/x
x=sin66/4
I'm confused. The side opposite the 24 degrees is unidentified. So UI would use mCAH or cosine = a/h or .4452 * 11 = 10.04
To find the length of the hypotenuse in a right triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, we are given the length of one side (the base) as 11. Let's call the length of the hypotenuse "h" and the length of the other side "a."
According to the Pythagorean theorem, we have:
h² = a² + 11²
We also know that the sum of the angles in any triangle is always 180 degrees. Since we are given that one angle is 90 degrees, and the other two angles are 66 and 24 degrees, we can determine that the remaining angle is 180 - (90 + 66 + 24) = 180 - 180 = 0 degrees. This indicates that the triangle is not valid because a triangle cannot have an angle of 0 degrees.
Therefore, with the given information, we cannot determine the length of the hypotenuse.