A right triangle has a 45 degree angle. The hypotenuse is x and the leg is 8. Find the value of x.
LOL 90 + 45 + other angle = 180
so other angle = 45
In other words we know from the start that it is an isoceles right triangle.
sides are 8
hypotenuse is 8 sqrt 2
because
1^2 + 1^2 = 2^2 :)
Well, it seems like we have a "right" angle and a "wrong" angle here. But don't worry, I won't "sine" away from giving you the answer!
In a right triangle with a 45-degree angle, the two legs are congruent. So, if one leg is 8, the other leg will also be 8.
Now, we can use the Pythagorean theorem to find the value of the hypotenuse. The theorem states that the square of the hypotenuse is equal to the sum of the squares of the two legs.
Thus, x^2 = 8^2 + 8^2 = 64 + 64 = 128.
Taking the square root of both sides, we find that x = √128.
And if you simplify √128, you'll end up with x ≈ 11.314, giving us a hypotenuse that's a little "irrational."
So, the value of x is approximately 11.314. Happy calculating!
In a right triangle, the hypotenuse is the longest side and is opposite the right angle. The other two sides are called the legs.
Given that the triangle has a 45-degree angle, we can use the properties of a 45-45-90 triangle. In a 45-45-90 triangle, the two legs are congruent and the hypotenuse is equal to √2 times the length of one of the legs.
In this problem, one leg has a length of 8. Therefore, the hypotenuse (x) is equal to √2 times 8.
Calculating this, we have:
x = √2 * 8
Simplifying further:
x = 8√2
Thus, the length of the hypotenuse (x) is 8√2.
To find the value of the hypotenuse, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the two other sides (the legs).
In this case, one of the legs is 8 units long, and we need to find the length of the hypotenuse (which is denoted as x). Since the triangle has a 45-degree angle, we know that the other leg will also be 8 units long (since the angles in a right triangle add up to 90 degrees).
Using the Pythagorean theorem, we can write the equation:
x^2 = 8^2 + 8^2
Simplifying, we have:
x^2 = 64 + 64
x^2 = 128
To find the value of x, we can take the square root of both sides of the equation:
x = √128
Simplifying, we get:
x ≈ 11.31
Therefore, the value of x (the hypotenuse) is approximately 11.31 units.