If a right triangle has a leg that is 6 ft. long and the hypotenuse is 12 ft. long, how long is the other leg? Round to the nearest tenth.(1 point) correct answer this time
Let's use the Pythagorean theorem to solve this problem. According to the theorem, the sum of the squares of the lengths of the two legs of a right triangle is equal to the square of the length of the hypotenuse.
Let's denote the length of the other leg as x. Using the given information, we can set up the equation as follows:
6^2 + x^2 = 12^2
36 + x^2 = 144
x^2 = 144 - 36
x^2 = 108
Taking the square root of both sides, we find:
x ≈ √108
x ≈ 10.39
Rounded to the nearest tenth, the length of the other leg is approximately 10.4 ft.
Find the unknown side length in the given triangle. Round to the nearest hundredth.(1 point)
To find the unknown side length in the triangle, we can again use the Pythagorean theorem. Let's denote the length of the unknown side as x.
We have the length of one leg as 6 ft and the length of the hypotenuse as 12 ft. So we can set up the equation as follows:
6^2 + x^2 = 12^2
36 + x^2 = 144
x^2 = 144 - 36
x^2 = 108
Taking the square root of both sides, we find:
x ≈ √108
x ≈ 10.392
Rounded to the nearest hundredth, the length of the unknown side is approximately 10.39 ft.
Find the unknown side length in the given triangle. Round to the nearest hundredth.(1 point) correct answer
I apologize for the confusion in my previous responses. Let's solve the problem correctly this time.
In a right triangle, the Pythagorean theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the two legs.
Let's denote the length of the unknown side as x. Using the given information, we can set up the equation as follows:
x^2 + 6^2 = 12^2
x^2 + 36 = 144
x^2 = 144 - 36
x^2 = 108
Taking the square root of both sides, we find:
x ≈ √108
x ≈ 10.39
Rounded to the nearest hundredth, the length of the unknown side is approximately 10.39 ft.
Find the unknown side length in the given triangle. Round to the nearest hundredth.(1 point) one side is 20 and other side is 30 whats the other side
To find the unknown side length in the given triangle, we can again use the Pythagorean theorem. Let's denote the length of the unknown side as x.
The Pythagorean theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the two legs.
So, we have:
x^2 + 20^2 = 30^2
x^2 + 400 = 900
x^2 = 900 - 400
x^2 = 500
Taking the square root of both sides, we find:
x ≈ √500
x ≈ 22.36
Rounded to the nearest hundredth, the length of the unknown side is approximately 22.36.
Camila needs to fix the window on the front of her house. The bottom of the window is 16 ft. from the ground. She only has a 20 ft. ladder. How far from the base of the house should she set up the ladder so that the top of the ladder is exactly at the bottom of the window?(1 point) ft.
We can solve this problem by using the Pythagorean theorem. Let's denote the distance from the base of the house to where the ladder should be set up as x.
According to the Pythagorean theorem, the sum of the squares of the lengths of the two legs of a right triangle is equal to the square of the length of the hypotenuse.
In this case, the ladder acts as the hypotenuse, the distance from the base of the house to the bottom of the window acts as one leg (16 ft), and the distance from the base of the house to where the ladder should be set up acts as the other leg (x ft).
Using the given information, we can set up the equation as follows:
x^2 + 16^2 = 20^2
x^2 + 256 = 400
x^2 = 400 - 256
x^2 = 144
Taking the square root of both sides, we find:
x ≈ √144
x ≈ 12
Therefore, Camila should set up the ladder approximately 12 ft from the base of the house so that the top of the ladder is exactly at the bottom of the window.
To find the length of the other leg of the 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 (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).
In this case, we know that one leg is 6 ft. long (let's call it a), and the hypotenuse is 12 ft. long (let's call it c). We need to find the length of the other leg (let's call it b).
Using the Pythagorean theorem, we can set up the equation:
a^2 + b^2 = c^2
Substituting the given values:
6^2 + b^2 = 12^2
36 + b^2 = 144
To isolate b^2, we subtract 36 from both sides:
b^2 = 144 - 36
b^2 = 108
Now we can take the square root of both sides to solve for b:
b = sqrt(108)
Using a calculator, we find:
b ≈ 10.4 ft
Therefore, the length of the other leg, rounded to the nearest tenth, is approximately 10.4 ft.