Question

You sketch a right triangle that has a hypotenuse of 13 centimeters, and one leg that is 8 centimeters. How many centimeters is the other leg?

Answer 1

Hello from MrBillDoesMath!

Answer:

sqrt(105)

(which is approximately 10.25 centimeters )

Discussion:

Call the unknown leg"a". From the Pythagorean theorem

8^2 + a^2 = 13^2            => subtract 8^2 = 64 from both sides

a^2  = 13^2 - 64              => as 13^2 = 169

a^2  = 169 - 64 = 105     => take the square root of both sides

a = sqrt(105) which is approximately 10.25 centimeters

Thank you,

MrB

Answer 2

Answer:

Length of other leg is 10.25 cm

Step-by-step explanation:

The right angle triangle ABC that has a hypotenuse of 13 centimeters, and one leg that is 8 centimeters is attached below.

Let missing leg is x cm.

We can use Pythagorean  theorem to find the other leg.

$AC^2=AB^2+BC^2\\\\13^2=x^2+8^2\\\\169=x^2+64\\\\x^2=169-64\\\\x^2=105\\\\x=\sqrt{105}\\\\x=10.25$

Hence, the length of other leg is 10.25 cm