In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If b = 5 yards and c = 8 yards, what is a? If necessary, round to the nearest tenth.
a = ______ yards
In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If b = 5 yards and c = 8 yards, what is a? If necessary, round to the nearest tenth. a = ______ yards
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To find the length of leg ( a ) in a right triangle, we can use the Pythagorean theorem, which states:
[
a^2 + b^2 = c^2
]
Given:
– ( b = 5 ) yards
– ( c = 8 ) yards
We can substitute the values of ( b ) and ( c ) into the equation:
[
a^2 + 5^2 = 8^2
]
Calculating the squares:
[
a^2 + 25 = 64
]
Now, we can isolate ( a^2 ) by subtracting 25 from both sides:
[
a^2 = 64 – 25
]
[
a^2 = 39
]
To find ( a ), we take the square root of both sides:
[
a = sqrt{39} approx 6.2 text{ yards (rounded to the nearest tenth)}
]
So, the length of ( a ) is approximately 6.2 yards.