What is the length of the unknown leg in the right triangle?
A right triangle has a side with length 20 meters, hypotenuse with length 25 meters, and side labeled b.
StartRoot 5 EndRoot m
5 m
StartRoot 45 EndRoot m
15 m
The length of the unknown leg, labeled "b," in the right triangle is 15 meters.
In centimeters, what is the unknown length in this right triangle?
A right triangle with side length 60 centimeters, x, and hypotenuse of 61 centimeters.
To find the length of the unknown leg in centimeters, labeled "x," we can use the Pythagorean theorem. According to the theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, we have the side length of 60 centimeters, the unknown length "x," and the hypotenuse of 61 centimeters.
Using the Pythagorean theorem, we can set up the equation:
60^2 + x^2 = 61^2
Simplifying the equation, we have:
3600 + x^2 = 3721
Subtracting 3600 from both sides, we get:
x^2 = 121
Taking the square root of both sides, we find:
x = 11 centimeters
So, the length of the unknown leg, labeled "x," in centimeters is 11 centimeters.
Imara used these steps to find the length of the hypotenuse of the right triangle.
3 squares are positioned to form a right triangle. The small square is labeled 15, medium square is 20, and large square is not labeled.
Step 1: Find the area of the square with side lengths of 20: 400
Step 2: Find the area of the square with side lengths of 15: 225
Step 3: Find the sum of the areas of the two squares: 625
Step 4: State the length of the hypotenuse: 625
Which best describes Imara’s error?
She should have found the area of the square with side lengths of 15 first.
She did not correctly calculate the area of the square with side lengths of 15.
She should have found the sum of 15 and 20 and then squared the sum.
She did not find the side lengths of the square with an area of 625.
The error in Imara's steps can be attributed to the statement made in Step 4 where they state the length of the hypotenuse is 625. The hypotenuse cannot be equal to the sum of the areas of the squares as given in Step 3. The length of the hypotenuse should be the square root of the sum of the areas of the squares. So, the correct statement should be the square root of 625.
Reynaldo rode his bike 2 miles north and 3 miles east. Which equation should he use to find the distance, d, that takes him directly back home?
A triangle has side lengths 2, 3, and hypotenuse d.
2 squared + 3 squared = d squared
3 squared minus 2 squared = d squared
d squared + 2 squared = 3 squared
d squared + 3 squared = 2 squared
The correct equation Reynaldo should use to find the distance, "d," that takes him directly back home is:
2 squared + 3 squared = d squared
This equation is derived from 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 other two sides. In this case, the sides labeled 2 and 3 represent the distances Reynaldo rode, and "d" represents the distance back home.
How long a ladder must you have to reach the top of a 15-foot wall if the bottom of the ladder is placed 4 feet from the base of the wall? Round to the nearest tenth of a foot.
14.5 ft
15.5 ft
17.0 ft
19.0 ft
To find the length of the unknown leg, 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 other two sides.
In this case, we know the length of the hypotenuse (25 meters) and one of the sides (20 meters). Let's label the unknown leg as "b".
Using the Pythagorean theorem, we can write the equation as:
25^2 = 20^2 + b^2
Simplifying this equation, we have:
625 = 400 + b^2
Subtracting 400 from both sides, we get:
225 = b^2
To solve for b, we need to find the square root of both sides of the equation. However, we need to consider both the positive and negative square roots since we have a right triangle, and both sides can be positive or negative.
Taking the square root of both sides, we have:
√225 = √(b^2)
Simplifying further, we have:
15 = b
So, the length of the unknown leg (b) in the right triangle is 15 meters.