Question

A right triangle has side lengths of 0.6 meter and 0.8 meter. What is the length of the hypotenuse? Round to the nearest tenth.

A. 0.1 meter
B. 0.5 meter
C. 1.0 meter
D. 4.8 meters

Answer 1

Use the Pythagorean theorem since you are working with a right triangle:

a^2+b^2=c^2a2+b2=c2

The legs are a and b and the hypotenuse is c. The hypotenuse is always opposite the 90° angle. Insert the appropriate values:

0.8^2+0.6^2=c^20.82+0.62=c2

Solve for c. Simplify the exponents (x^2=x*xx2=x∗x ):

0.64+0.36=c^20.64+0.36=c2

Add:

1=c^21=c2

Isolate c. Find the square root of both sides:

\begin{gathered}\sqrt{1}=\sqrt{c^2}\\\\\sqrt{1}=c\end{gathered}1=c21=c

Simplify \sqrt{1}1 . Any root of 1 is 1:

c=c= ±11 *

c=1,-1c=1,−1

Answer 2

The length of the hypotenuse is 1 meter. Option C

To determine the value of the hypotenuse, we have to follow the rule of the Pythagorean theorem which states that the square of the hypotenuse side is equal to the sum of the squares of the other two sides.

Then, we have that;

h² = 0.8²+ 0. 6²

find the squares and substitute the values, we have

h² = 0.64 + 0.36

add the values, we get;

h²= 1

find the square root of both sides

h =1meter