What is the length of the third side of a rt triangle if one side is 8cm and the hypotenuse is 16cm?

Answer 1

Let us consider opposite side=8 cm in a rt triangle .
sin theta=opposite side/hypotenuse
=8/16
=1/2
sin theta =0.5
theta=sin inv.(0.5)=30 degree

Now ,cos theta
=adjacent side/hypotenuse
cos 30 =adjecent side/16
cos 30 * 16= adjecent side
Adjecent side=0.866*16=13.856 cms

Answer 2

Remember the Pythagoras Theorum? Well, it's a^2 + b^2=c^2 if you don't. The hypotenuse is the c^2 (it has to be). So one side is 8cm. So let it be the a or b. It doesn't matter. So you'd get this:
8^2+b^2=16^2(Pyth. Thm.)
64+b^2=256
b^2+64-64=256-64
b^2=192
Wait, did you get the question wrong? The answer on my calculator is 13.85640646...and the answer shouldn't have so many figures after the decimal...

Answer 3

Here's a way to do this without using the Pythagorean theorem.
Note that the 8cm side is half the hypotenuse. So this
is a 30-60-90 right triangle. Thus the third side is
16 sin 60 = 8*sqrt(3).
(All angles are in degrees here.)

Answer 4

Use the Pythagorean theorem, a^2+b^2=c^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

You have a=8 cm, c=16 cm, and b is the length of the third side.

That means 8^2+b^2=16^2, or 64+b^2=256.

So, b^2=256-64=192, meaning

b = sqrt(192) = sqrt(64*3)
=8*sqrt(3) cm=13.85640646055102 cm.

Answer 5

from Pythagoras theorem:
h^2=a^2+b^2
or
b^2=h^2-a^2
b^2=16^2-8^2=256-64=192
b=sqrt(192)=8*sqrt(3)=13.9cm
this is a 30, 60, 90 rt triangle.

Answer 6

Using the Pythagoras theorem, the length of the third side can be calculated.
The length comes to around 13.85640646 cm

Answer 7

(16)2 -(8)2 = 256-64=192
root 192=13.8

Answer 8

a^2 + b^2 = c^2

a^2 + 8^2 = 16^2

a = 13.86

Answer 9

a squared= c squared- b2
a squared= 16 squared - 8 squared
a squared= 256- 64
a squared= 192
a= square root of 192
a=13.856

Answer 10

(Hypothenuse)^2=(first side)^2+(second side)^2

So (second side) = sqrt ( 256 -64 ) = sqrt ( 192) = 13.86