 (not to scale)

The triangle ABC is inscribed within a square. If A=72º and B=84º, find the other angles in the figure (round to 2 decimal places if necessary).

Sir,

Is this solution correct?

https://ibb.co/jyBnNZB

Edit:

https://ibb.co/jgncxfG
https://ibb.co/8D0fVKF

The last line has an error it should be

x = 114*sin72/(sin72+sin84)

And x turns out to be 55.726586093

rest can be easily calculated
ago by Level 4 User (5.8k points)
edited ago

No, it isn’t. Remember that the triangle is inside a square, not a rectangle! Hint: you can use the Sine Rule to work out the relative lengths of the sides and then build up equations based on the fact that all sides of the square are equal.

Actually that was the first thing that I did,

Please have a look at the edit.
Also Sir,

What was wrong with this approach?

https://ibb.co/tbgfDZg

Edit: Okay I get it, my initial assumption was wrong.

Please validate my edited post above.

Thank You

No, unfortunately still not right. In my solution I did not find it necessary to draw any additional construction lines. It was all done through trigonometry. Yes, you’re right: given one angle you can derive all the others by simple arithmetic. There is only one solution. The clue is that the “bare” sides of the square can each be expressed in terms of one unknown angle. That gives you an equation, which needs to be simplified by using trig identities and a bit of manipulation to solve for the unknown angle. I have only glanced at your workings out so far, but I’ll take a closer look to see what assumptions you made.

And what about the edit in original answer, did you look at that?

It is done using the law of sines.

I note that in equation (II) you have x instead of sin(x).

You don’t need the Sine Rule in a right triangle. So, for example, m=bsin(x) by definition of sine, and m=acos(x-24), which means that bsin(x)=acos(x-24). You have the right idea.

When you find x, check your answer by computing the lengths of the sides of the square after working out all the angles, and make sure that the sides are in fact equal.