Question

A right triangle has legs of 5 ft and 6 ft. What is the length of the hypotenuse? _____ ft.

1.) 1.0
2.) 7.8
3.) 11.0
4.) 3.3

Answer 1

2. 7.8

Explanation:

Since this is a right triangle, use Pythagorean Theorem.

a^2+b^2=c^2

where a and b are the legs, and c is the hypotenuse.

The legs of the triangle are 5 ft and 6 ft. Therefore, 5 and 6 are a and b. The hypotenuse is unknown, so it can be left as c.

5^2+6^2=c^2

Evaluate the exponents

25+36=c^2

Add

61=c^2

Since we are trying to find c, we have to get c by itself. Since c is being squared, take the square root of both sides

√61=√c^2

√61=c

7.81024967591=c

Rounded to the nearest tenth:

7.8=c

The hypotenuse is about 7.8 feet

Answer 2

2.) 7.8

Explanation:

We can use Pythagorean theorem

a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse

5^2 + 6^2 = c^2

25+36 = c^2

61 = c^2

Take the square root of each side

sqrt(61) = sqrt(c^2)

7.810249676 = c