Find each missing length. Round to the nearest tenth, if necessary.
A right triangle has a leg labeled, x, a leg measuring 16 feet, and a hypotenuse measuring 20 feet.
A right triangle has a leg measuring 20 inches, a leg labeled, x, and a hypotenuse measuring 25 inches.
A right triangle has a leg measuring 12 meters, a leg labeled, y, and a hypotenuse measuring 15 meters.
A right triangle has a leg measuring 14 centimeters, a leg measuring 50 centimeters, and a hypotenuse labeled, c.
1st one:
x^2 + 16^2 = 20^2
x^2 = 400 - 256 = 144
x = 12 , SO THE BOT IS WRONG AGAIN
2nd one:
x^2 + 20^2 = 25^2
x^2 = 625-400 = 225
x = 15, SO THE BOT IS WRONG
3rd ....
...
x = 9 THE BOT IS WRONG AGAIN
4th
THE BOT IS WRONG AGAIN
0/4 , that's awfull
AAAaannndd the bot gets it wrong yet again!
For the first three, think of the 3-4-5 right triangle, scaled up
for the last one, use the 7-24-25 triangle
memorize a few of these basic triples, and you can save yourself some calculation.
To find the missing length in each right triangle, we can use the Pythagorean theorem, which 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 two legs.
1. For the first right triangle:
The leg labeled 'x' is missing. We know that one leg is 16 feet and the hypotenuse is 20 feet. We can use the Pythagorean theorem to find the missing length:
x^2 + 16^2 = 20^2
Simplifying the equation:
x^2 + 256 = 400
Subtracting 256 from both sides:
x^2 = 144
Taking the square root of both sides:
x = 12
So, the missing length 'x' in the first right triangle is 12 feet.
2. For the second right triangle:
The leg labeled 'x' is missing. We know that one leg is 20 inches and the hypotenuse is 25 inches. Using the Pythagorean theorem:
x^2 + 20^2 = 25^2
Simplifying the equation:
x^2 + 400 = 625
Subtracting 400 from both sides:
x^2 = 225
Taking the square root of both sides:
x = 15
Therefore, the missing length 'x' in the second right triangle is 15 inches.
3. For the third right triangle:
The leg labeled 'y' is missing. We know that one leg is 12 meters and the hypotenuse is 15 meters. Applying the Pythagorean theorem:
y^2 + 12^2 = 15^2
Simplifying the equation:
y^2 + 144 = 225
Subtracting 144 from both sides:
y^2 = 81
Taking the square root of both sides:
y = 9
Hence, the missing length 'y' in the third right triangle is 9 meters.
4. For the fourth right triangle:
The hypotenuse labeled 'c' is missing. We know that one leg is 14 centimeters and the other leg is 50 centimeters. We will use the Pythagorean theorem:
14^2 + 50^2 = c^2
Simplifying the equation:
196 + 2500 = c^2
Adding 196 and 2500:
2696 = c^2
Taking the square root of both sides:
c = √2696 ≈ 51.92
Hence, the missing length 'c' in the fourth right triangle is approximately 51.92 centimeters.
x = 17.2 feet
x = 22.5 inches
y = 13.4 meters
c = 56.6 centimeters