Question

I need help. I'm studying pre calculus and I have to a missing variable of a non right triangle with either law of sine or cosine, but one side is x, the other side is missing and the other side is 10, and I only have one given angle, which is 28? How do I know whether to use law of sine or cosine, and how I do I use law of sine or cosine to find my missing variable?

Answer 1

First off i just want to say that both the Sine and Cosine rule can be used in any triangle (not just right-angled triangles) but the Sine rule can only be used if a side and its opposite angle are known. (which it isn't) So you are going to be using the Cosine rule

Here is an example with steps

"Work out angle P° in the diagram below:"
http://www.cimt.plymouth.ac.uk/projects/mepres/step-up/sect4/egcosinerule2.gif

Step 1 Start by writing out the Cosine Rule formula for finding angles:
cos(A) = b2 + c2 - a2/2bc

Step 2 Fill in the values you know, and the unknown length:
cos(P°) = 52 + 82 – 72/2 × 5 × 8
Remember to make sure that the terms on top of the fraction are in the correct order.

Step 3 Evaluate the right-hand-side and then use inverse-cosine (cos–1) to find the angle:
cos(P°) = 52 + 82 – 72/2 × 5 × 8
cos(P°) = 0.5
P° = cos–1(0.5) = 60° (3sf)

If you know two sides and an angle which is not inbetween them then you can use the Cosine Rule to find the other side, but it is easier to use the Sine Rule in this situation – you should always use the Sine Rule if you have an angle and its opposite side.

Answer 2

Now please tell me that your trying to find the missing angle. Because if i just typed this out for no reason that would be a fail by me....

Answer 3

No, I'm trying to find two missing sides of a non right triangle. One side is a variable x which is what I'm trying to find. The other side is 10, and I have a missing side. I only have one given angle which is 28. I'm trying to find out whether I use law of sine or cosine to find my missing variable and what are the steps.

Answer 4

28 is the only given angle

Answer 5

I dont know if you still need the answer but if your trying to find the side you need to know the other two sides and the opposite angle. Which in the picture I only see the sides, but you did say that one angle is 28 so this should work.

To answer your main question you need to use the version of the COSINE Rule where a2 is the subject of the formula:
a2 = b2 + c2 – 2bc cos(A)
Side a is the one you are trying to find. Sides b and c are the other two sides, and angle A is the angle opposite side a.
Heres another example on how to do this:

Work out the length of x in the diagram below:
http://www.cimt.plymouth.ac.uk/projects/mepres/step-up/sect4/egcosinerule1.gif

Step 1 Start by writing out the Cosine Rule formula for finding sides:
a2 = b2 + c2 – 2bc cos(A)

Step 2 Fill in the values you know, and the unknown length:
x2 = 222 + 282 – 2×22×28×cos(97°)
(It doesn't matter which way around you put sides b and c – it will work both ways so dont worry about that.)

Step 3 Evaluate the right-hand-side and then square-root to find the length:
x2 = 222 + 282 – 2×22×28×cos(97°)
(evaluate the right hand side)
x2 = 1418.143.....
(square-root both sides)
x = 37.7 (accurate to 3 significant figures)
Just like the Sine Rule you have to try and keep full accuracy until the end of your calculation to so that you dont make mistakes.

I sure hope this is what your looking for this time! If it is then I was glad to help. : )

Answer 6

one other thing... In the picture you posted it looks as if it is a right triangle? If this is true then you have both the 28 deg. and 90 deg. (Just a heads up)

Answer 7

This a not a right triangle. Its an oblique triangle. And there is only one given side and angle. I mean I know how to use the law of sine and cosine when there is two given sides and an angle, but I only have one given side which is 10.