Question

which of the following represents the length, in ft, of the second leg of a right triangle that has a hypotenuse length of 95 ft and another leg length of 76 ft?
reference sheet
a = πr²
c = 2πr
a = lw
a = 1/2bh
c² = a² + b²
special right triangles
v = lwh
v = πr²h
v = 4/3πr³
v = 1/3πr²h
v = 1/3lwh
the number of degrees of arc in a circle is 360.
the number of radians of arc in a circle is 2π.
the sum of the measures in degrees of the angles of a triangle is 180.
19
57
122
3249

Explanation:

Step1: Apply Pythagorean theorem

Let the hypotenuse be $c = 95$, one leg be $a=76$, and the other leg be $b$. According to the Pythagorean theorem $c^{2}=a^{2}+b^{2}$, so $b^{2}=c^{2}-a^{2}$.

Step2: Substitute values

Substitute $c = 95$ and $a = 76$ into the formula: $b^{2}=95^{2}-76^{2}=(95 + 76)(95 - 76)$ (using the difference - of - squares formula $x^{2}-y^{2}=(x + y)(x - y)$). Then $b^{2}=(171)\times(19)=3249$.

Step3: Solve for $b$

Take the square root of both sides: $b=\sqrt{3249}=57$ (we take the positive value since length cannot be negative).

Answer:

$57$