In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If a = 7 feet and c = 10 feet, what is b? If necessary, round to the nearest tenth.
b = ____ feet
In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If a = 7 feet and c = 10 feet, what is b? If necessary, round to the nearest tenth. b = ____ feet
Share
To find the length of side b in a right triangle, we can use the Pythagorean theorem, which states that (a^2 + b^2 = c^2).
Given:
– (a = 7) feet
– (c = 10) feet
We can substitute the values into the formula:
[
7^2 + b^2 = 10^2
]
Calculating the squares:
[
49 + b^2 = 100
]
Now, subtract 49 from both sides:
[
b^2 = 100 – 49
]
[
b^2 = 51
]
Next, take the square root of both sides to solve for b:
[
b = sqrt{51} approx 7.1 text{ feet (rounded to the nearest tenth)}
]
So, the length of b is approximately 7.1 feet.