# Thread: Help me find the angle

1. ## Help me find the angle

So we have a R-H triangle, the hypotenuse is $\displaystyle 5cm$and the 1 of the angles measures$\displaystyle \frac {1}{8} \pi$

heres how i found the 3rd angle (x), in radians:
$\displaystyle \frac{1}{8} \pi = 22.5°$

so angle is $\displaystyle 90°- 22.5° = 67.5°$

$\displaystyle sin22.5 = \frac {5}{x} , so x = \frac {5}{sin22.5} = 13.06°$ or .228 radians

Is this right, and how could i find the answer to my question without converting to degrees?

More over how could i find the length of the other two sides?

Thanks

So we have a R-H triangle, the hypotenuse is $\displaystyle 5cm$and the 1 of the angles measures$\displaystyle \frac {1}{8} \pi$

heres how i found the 3rd angle (x), in radians:
$\displaystyle \frac{1}{8} \pi = 22.5°$

so angle is $\displaystyle 90°- 22.5° = 67.5°$

$\displaystyle sin22.5 = \frac {5}{x} , so x = \frac {5}{sin22.5} = 13.06°$ or .228 radians

Is this right, and how could i find the answer to my question without converting to degrees?

More over how could i find the length of the other two sides?

Thanks
Yeah, degrees never should have came into the picture.

Angle three is given by

$\displaystyle \overbrace{\frac{\pi}{2}}^{90^\circ}-\frac{\pi}{8}=\frac{4\pi}{8}-\frac{\pi}{8}=\frac{3\pi}{8}$

Understand?

3. ## correction

sin(22.5)=x/5
so x=5sin(22.5) and similarly other side will be
y=5cos(22.5)
if 0ne angle is pi/8 other will be (pi/2)-(pi/8)=3pi/8
you may calculate sin(3pi/8) if you don't want degree system.

4. Originally Posted by VonNemo19
Yeah, degrees never should have came into the picture.

Angle three is given by

$\displaystyle \overbrace{\frac{\pi}{2}}^{90^\circ}-\frac{\pi}{8}=\frac{4\pi}{8}-\frac{\pi}{8}=\frac{3\pi}{8}$

Understand?
Not really - so your saying

$\displaystyle \frac{3\pi}{8}$

is the size of the third angle?

Not really - so your saying

$\displaystyle \frac{3\pi}{8}$

is the size of the third angle?

it is .

6. So how do i find the lengths of the other two sides?

So how do i find the lengths of the other two sides?

By doing some trigo .

$\displaystyle \sin \frac{\pi}{8}=\frac{x}{5}$

Then use the phythagoras theorem to get the other side .

8. Im seriously at a loss with this, thank you for your help up to now, but can you talk me through it

9. $\displaystyle \pi$ radians is equal to 180 degrees

your calculator can most probably calculate sine of this using degrees or radians.

one angle is $\displaystyle \frac{\pi}{8}$

$\displaystyle sin(\frac{\pi}{8})=\frac{opposite}{hypotenuse}=\fr ac{x}{5}$

$\displaystyle x=5sin(\frac{\pi}{8})=1.9134cm$

There are two ways to find the other side;
$\displaystyle cos(\frac{\pi}{8})=\frac{adjacent}{hypotenuse}=\fr ac{y}{5}$

and $\displaystyle y=5cos(\frac{\pi}{8})=5(0.9239)=4.61939cm$

or you could use pythagoras' theorem.

$\displaystyle y^2+(1.9134)^2=5^2$
$\displaystyle y^2=21.339$
$\displaystyle y=4.16194cm$

to find the other angle working in radians

$\displaystyle \frac{\pi}{2}=\frac{180}{2}=90degrees$
so
$\displaystyle \frac{\pi}{2}-\frac{\pi}{8}=\frac{3\pi}{8}radians$

$\displaystyle \frac{3\pi}{8}=\frac{3(180)}{8}=67.5degrees$

which is what you got as your other angle.

did i leave anything out?

10. so the other two lengths are:

1.9134cm & 4.61939cm ?

11. yes