Finding Theta and Beta

[jman15]

Ok so there is a non-equilateral triangle. All three sides are labeled. The side on the left is 14, the side on the right is 8, and the bottom is 19. It asks you to find theta which is the angle between 14 and 19. Then it asks you to find beta which is between 14 and 8.

How would i do this and what is the correct answer?

 

[mmm4444bot]

Look up "Law of Cosines".

Are you in a math class? Do you have a textbook?

 

[jman15]

Yes i am but my teacher is not good. I am just trying to do this problem by myself for extra credit

 

[mmm4444bot]

just trying to do this problem by myself for extra credit

Cool.

After you use the Law of Cosines to discover that cos(?) = 493/532, you'll need to use a calculator's inverse cosine function to get the angle ? (in radians).

 

[jman15]

I worked my way through the problem and am stuck when i get to c^2=25 cos C

What do i do here?

or did i do it right?

 

[mmm4444bot]

i get to c^2=25 cos C Nope.

It looks like you're using C for theta, right? That's okay.

And, the value of c is 8, so I'm not sure why you're typing c^2 instead of 8^2.

On these boards, you'll find that time is saved, if you show your work. Without seeing it, I can't tell where you went wrong.

When we use the Law of Cosines with an angle theta, then the triangle side opposite angle theta is always the side^2 that appears in the formula all by itself on one side of the equals sign.

$\displaystyle a^2 \;=\; b^2 \;+\; c^2 \;-\; 2 \ b \ c \ cos(\theta)$ ? Use this form when side a is opposite theta.

$\displaystyle b^2 \;=\; a^2 \;+\; c^2 \;-\; 2 \ a \ c \ cos(\theta)$ ? Use this form when side b is opposite theta.

$\displaystyle c^2 \;=\; a^2 \;+\; b^2 \;-\; 2 \ a \ b \ cos(\theta)$ ? Use this form when side c is opposite theta.

Try the Law of Cosines again, plugging the values a = 14, b = 19, and c = 8 into the third form listed above because side c is opposite theta, in this exercise.

If you cannot simplify to cos(C) = 493/532, please show your work.

Cheers ~ Mark

 

[jman15]

i simplified and then inversed to get 22.18

is that right?

 

[mmm4444bot]

i simplified and then inversed to get 22.18

is that right? Yes, but it's not properly rounded.

Theta = 22.08 degrees, if you were told to round to the nearest hundredth of a degree.

Now that you know one of the angles, you can use the Law of Sines to write and solve a proportion for Beta.