Question

Given a right triangle with a hypotenuse of 6 cm and a leg of 4cm, what is the measure of the other leg of the triangle rounded to the tenths?

Answer 1

4.5 cm

Explanation:

Since this is a right triangle, we can use the Pythagorean Theorem.

`a^2+b^2=c^2`

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

One leg is unknown and the other is 4 cm. The hypotenuse is 6 cm.

`a=a\\b=4\\c=6`

Substitute the values into the theorem.

`a^2+4^2=6^2`

Evaluate the exponents first.

4^2= 4*4= 16

`a^2+16=6^2`

6^2=6*6=36

`a^2+16=36`

We want to find a, therefore we must get a by itself.

16 is being added on to a^2. The inverse of addition is subtraction. Subtract 16 from both sides of the equation.

`a^2+16-16=36-16\\\\a^2=36-16\\\\a^2=20`

a is being squared. The inverse of a square is a square root. Take the square root of both sides.

`√(a^2)=√(20) \\\\a=√(20) \\\\a=4.47213595`

Round to the nearest tenth. The 7 in the hundredth place tells us to round the 4 in the tenth place to a 5.

`a=4.5`

Add appropriate units. In this case, centimeters.

a= 4.5 cm

The length of the other leg is about 4.5 centimeters.

Answer 2

4.5 cm

Explanation:

a^2+b^2=c^2

A represents the leg we already know, which has a length of 4 cm. C represents the hypotenuse with a length of 6 cm:

4^2+b^2=6^2, simplified: 16+b^2=36

subtract 16 from both sides:

b^2=20

now find the square root of both sides and that is the length of the other leg.

sqrt20= 4.4721, which can be rounded to 4.5