In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If a = 2 yards and c = 3 yards, what is b? If necessary, round to the nearest tenth.
b = _____ yards
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In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If a = 2 yards and c = 3 yards, what is b? If necessary, round to the nearest tenth.
b = _____ yards
To find the length of leg b in a right triangle where you know the lengths of leg a and the hypotenuse c, you can use the Pythagorean theorem, which states:
[ a^2 + b^2 = c^2 ]
Given:
– ( a = 2 ) yards
– ( c = 3 ) yards
Now, plug in the values:
[ (2)^2 + b^2 = (3)^2 ]
This simplifies to:
[ 4 + b^2 = 9 ]
Now, subtract 4 from both sides:
[ b^2 = 9 – 4 ]
[ b^2 = 5 ]
Next, take the square root of both sides to find b:
[ b = sqrt{5} ]
Calculating that gives:
[ b approx 2.236 ]
Rounding to the nearest tenth:
[ b approx 2.2 ]
So, the length of b is approximately 2.2 yards.