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
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
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To find the length of leg b in a right triangle, we can use the Pythagorean theorem, which states:
[ a^2 + b^2 = c^2 ]
Given that:
– ( a = 4 ) inches
– ( c = 7 ) inches
We can rearrange the formula to find b:
1. Substitute the values into the equation:
[ 4^2 + b^2 = 7^2 ]
[ 16 + b^2 = 49 ]
2. Subtract 16 from both sides:
[ b^2 = 49 – 16 ]
[ b^2 = 33 ]
3. Take the square root of both sides:
[ b = sqrt{33} ]
4. To round to the nearest tenth:
[ b approx 5.7 ] inches
So, the length of leg b is approximately 5.7 inches.