How do I do this question on trigonometry?

Question

If x is an acute angle and sin x = 12/13, find the values of tan x.

and if you can, this one too

If x is an obtuse angle and sin x = 3/5, the values of cos x.

Thank you!

Answer 1

1) Since the angle is acute (< 90) then sin x = opposite/hypotenuse.

So opp = 12, hypotenuse = 13.  Using Pythagoras theorem the base is sqrt(13*13 - 12*12) = 5

Hence tan x = Base / Hypotenuse = 5/13  

2) The next one I am not so sure but it may be 4/5 but please double check.

Answer 2

sin = opposite/ hypotenuse

tan = opposite/ adjacent

cos = adjacent/ hypotenuse

So if sin x = 12/13,

The side opposite x is 12 while the hypotenuse is 13.

So to find tan x,

we use the above equation and we get

opposite/ adjacent = 12/ A

We find that we don't know the value of A (adjacent). To find it, we use the Pythagoras' Theorem. I know using this method, the triangle has to be a right-angle one but in this case, x is not the right angle since its an acute triangle so another angle is the right angle. Just draw out the diagram and you will know what I mean. I hope this has helped you greatly! :)

For your second question, if sin x = 3/5,

The side opposite x is 3 while the hypotenuse is 5.

So to find cos x,

we use the above equation and we get

adjacent/ hypotenuse = A/ 5

Like your previous question, we have to use the Pythagoras' Theorem to find the value of A. Just keep in mind the concept and I'm sure you can do it! :)

Answer 3

Use your calculator...