Question

One of the legs of a right triangle measures 13 cm and the other leg measures 1 cm. Find the measure of the hypotenuse. If necessary, round to the nearest tenth.

Answer 1

Answer:

hypotenuse = 13.0 cm

Step-by-step explanation:

Given the dimensions of a right triangle whose legs have measures of 13 cm and 1 cm, we can use the Pythagorean Theorem to find the measure of the triangle's hypotenuse.

The Pythagorean Theorem states that the squared measure of a right triangle's hypotenuse is equal to the sum of the squared lengths of its legs. In other words:

Pythagorean Theorem:   c² = a² + b²

Let c = hypotenuse

     a  =  Leg₁   = 1 cm

    b  =  Leg₂  =  13 cm

Substitute these values into the given formula to find the measure of the hypotenuse, c:

c² = a² + b²

c² = ( 1 )² + (13)²

c² = 1 + 169

c² = 170

Next, take the square root of c² and 170 to isolate c:

$\displaystyle\mathsf{\sqrt{c^2}\:=\:\sqrt{170}}$

c = 13.04 or 13.0 cm

Therefore, the length of the hypotenuse is 13.0 cm.