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 when you know the lengths of both legs (a) and the hypotenuse (c), you can use the Pythagorean theorem, which states:
[ a^2 + b^2 = c^2 ]
Given:
– a = 4 inches
– c = 7 inches
Substituting the values into the equation:
[ 4^2 + b^2 = 7^2 ]
[ 16 + b^2 = 49 ]
Now, subtract 16 from both sides:
[ b^2 = 49 – 16 ]
[ b^2 = 33 ]
Next, take the square root of both sides to find b:
[ b = sqrt{33} ]
Calculating the value:
[ b approx 5.7 text{ inches} ]
So, the length of leg b is approximately 5.7 inches.