In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If a = 9 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 = 9 feet and c = 10 feet, what is b? If necessary, round to the nearest tenth. b = ____ feet
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To find the length of the leg ( b ) in a right triangle, we can use the Pythagorean theorem, which states that ( a^2 + b^2 = c^2 ).
Given:
– ( a = 9 ) feet
– ( c = 10 ) feet
We can rearrange the formula to solve for ( b ):
[
b^2 = c^2 – a^2
]
Now, let’s plug in the values:
[
b^2 = 10^2 – 9^2
]
[
b^2 = 100 – 81
]
[
b^2 = 19
]
Next, take the square root of both sides to find ( b ):
[
b = sqrt{19} approx 4.4 text{ feet}
]
Thus, the length of ( b ) is approximately 4.4 feet.