17.1 meters
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean Theorem.
![a^2+b^2=c^2](/tpl/images/0704/3309/7bfa7.png)
where a and b are the legs and c is the hypotenuse.
6 and 16 are the legs, because they form the right angle. c is the hypotenuse because it is opposite the right angle.
![6^2+16^2=c^2](/tpl/images/0704/3309/8b06f.png)
Evaluate the exponents.
6^2= 6*6= 36
16^2= 16*16= 256
![36+256=c^2](/tpl/images/0704/3309/96334.png)
Add 36 and 256.
![292=c^2](/tpl/images/0704/3309/cb094.png)
Since c is being squared, take the square root of both sides of the equation. The exponent and square root will cancel and leave c by itself
![\sqrt{292} =\sqrt{c^2}](/tpl/images/0704/3309/30344.png)
![\sqrt{292}=c](/tpl/images/0704/3309/19f1e.png)
![17.0880075=c](/tpl/images/0704/3309/0c01c.png)
Round to the nearest tenth. The 8 in the hundredeth place tells us to roung the 0 in the tenth place up to a 1.
![17.1=c](/tpl/images/0704/3309/ca2ee.png)
c= 17.1 m
The missing length, or the hyptenuse is 17.1 meters.