Question

5 multiple choice 1 point 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. 3249 19 57 122

Explanation:

Step1: Apply Pythagorean theorem

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

Step2: Substitute values

$b^{2}=95^{2}-76^{2}=(95 + 76)(95 - 76)$ (using the difference - of - squares formula $x^{2}-y^{2}=(x + y)(x - y)$).
$95+76 = 171$ and $95 - 76=19$, then $b^{2}=171\times19 = 3249$.

Step3: Find the value of $b$

$b=\sqrt{3249}=57$.

Answer:

C. 57