In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If a = 4 inches and c = 7 inches, what is b? If necessary, round to the nearest tenth.
b = ____ inches
What is the length of the other leg of the right triangle if given the lengths of one leg and hypotenuse?
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To find the length of leg ( b ) in a right triangle when you know the lengths of ( a ) (4 inches) and ( c ) (7 inches), you can use the Pythagorean theorem, which states:
[
a^2 + b^2 = c^2
]
1. Substitute the known values into the equation:
[
4^2 + b^2 = 7^2
]
2. Calculate the squares:
[
16 + b^2 = 49
]
3. Subtract 16 from both sides:
[
b^2 = 49 – 16
]
[
b^2 = 33
]
4. Now take the square root of both sides to find ( b ):
[
b = sqrt{33} approx 5.7 text{ inches}
]
So, the length of leg ( b ) is approximately 5.7 inches.