Question

the hypotenuse of a right triangle has length 50 cm. one leg has length 20 cm. to the nearest tenth, what is the length of the other leg? a. 30.0 cm b. 45.8 cm c. 49.8 cm d. 53.9 cm

Explanation:

Step1: Apply Pythagorean theorem

Let the hypotenuse be $c$, one leg be $a$ and the other leg be $b$. The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$. We know $c = 50$ cm and $a=20$ cm. Then $b^{2}=c^{2}-a^{2}$.

Step2: Substitute values

$b^{2}=50^{2}-20^{2}=2500 - 400=2100$.

Step3: Solve for $b$

$b=\sqrt{2100}\approx45.8$ cm.

Answer:

B. 45.8 cm