Question

Bit Confused on how to work out a geometry problem.

So I have a problem where I have to find the degree of angle A. I'm given that Angle C is a right angle, and the length of the hypotenuse and opposite angle.
Is there any formula I could use that would help me solve this because I'm just stuck on this question.
Thanks to anyone that helps.

Answer 1

Yep you can use trigonometry

Answer 2

Can you mark the things you are given in the above figure?

Answer 3

Thats what I was given.
I also think I'm supposed to divide the opposite angle by the hypotenuse to get the sine, but I'm not sure what to do after that.

Answer 4

Hmm good work so far!

see:

\[\sin x = \cfrac{AC}{AB}\]

Answer 5

Now, you know the value of AC and AB, so you can calculate sin x

Then using a calculator you can find out x!

(Hint: x = arcsin (AC/AB))

Answer 6

So would that be 12/31 or .38709...
I just started working on these problems today so I'm struggling a bit.

Answer 7

Good work!

Answer 8

Now, using a calculator:

x = arcsin (0.38709) = 67.226 degrees

Answer 9

Any doubt ?

Answer 10

Now, use the fact that:

Sum of all angles of a triangle = 180 deg

You know B and C, so can you find out A ?

Answer 11

A little, I'm a bit confused on what an arcsine is.

Answer 12

It basically is \(\sin^{-1}\)

For example:

sin (30 deg) = 1/2 = 0.5

=> 30 deg = \(\sin^{-1} (0.5)\) or arcsin (0.5)

Answer 13

Ok I think i'm starting to get it.
Also to what you said above, angle A would be 22.774 degrees.

Answer 14

Great work!!!! You are perfectly correct!!

Answer 15

Thank you!
I've spent the past hour going through online resources and haven't been able to understand it.

Answer 16

your welcome :)