In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If b = 72 miles and c = 97 miles, what is a? If necessary, round to the nearest tenth.
a = ___ miles
What is the length of leg a in a right triangle if leg b is 72 miles and the hypotenuse is 97 miles?
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To find the length of leg ( a ) in a right triangle when you know the lengths of leg ( b ) and the hypotenuse ( c ), you can use the Pythagorean theorem, which states:
[
a^2 + b^2 = c^2
]
In this case, you’re given:
– ( b = 72 ) miles
– ( c = 97 ) miles
First, square both ( b ) and ( c ):
[
b^2 = 72^2 = 5184
]
[
c^2 = 97^2 = 9409
]
Now, plug these values into the Pythagorean theorem and solve for ( a^2 ):
[
a^2 + 5184 = 9409
]
Subtract ( 5184 ) from both sides:
[
a^2 = 9409 – 5184 = 4225
]
Now, take the square root of ( a^2 ) to find ( a ):
[
a = sqrt{4225} = 65
]
So, the length of leg ( a ) is ( 65 ) miles.
Thus, the answer is:
a = 65 miles.