[Yusf]

Hello! Can anyone give me a theory that relates 3 angles of a triangle with a side?

[Wondergirl]

a formula?

[Yusf]

Yes. That's all I need.

[Wondergirl]

If you know three angles, that won't help you figure out the length of a side. Do you know at least one side?

[Yusf]

The question is like this.
Assume a pole AB with Point C and D on 2 sides of it. If they are joined with A and B, We get 2 right angled triangles, ACB and ADB. Joining C and D gives right angled Triangle BCD at the base. Given that CD=200, angle ACB=15° and angle ADB=25° find the height of AB.

[Wondergirl]

Are you taking trig?

Did you draw a picture?

[Yusf]

Yes its trig. I can draw a picture but how can I upload it here?

[Wondergirl]

Yes its trig. I can draw a picture but how can I upload it here?

Does anything on this page help?

Solving Triangles

[ebaines]

I am unable to follow your description of the problem (I have no idea what you mean by "Assume a pole AB with Point C and D on 2 sides of it"). It would really help if you could post a figure. Nevertheless, since you have one length given, have the various angles and want to find the length of another side of one of the triangles, you should be able to use the Law of Sines - for any triangle with side lengths A, B and C and angles a, b, and c:



I'm guessing that from the figure you should be able to relate the 200' length of CD to the length of one of the sides of the triangle ABC or ABD. in order to determine length AB.

[Yusf]

No. The I know the theories but can't use them as two measurements are not given. I tried The site wondergirl suggested Let me try to explain. For this example, names I use may be differrent from the ones I used earlier. Assume you drew a triangle BCD on the floor . CD is towards you and B is away from you. You insert a pole in B and tie rope from top of the pole A to C and A to D. Now we get triangle ACB on left and ADB on right and Bcd on bottom. This is the figure. Here angle CBD is 90° angle ACB is 15° and angle ADB is 25°.Line Cd is 200. Now I need the length of the pole.

[ebaines]

The height of the pole AB is equal to the length of BC times tan(15), and it's also equal to length BD times tan(25). Hence length BC= BD x tan(25)/tan(15). Now we can use Pythagoras on triangle BCD: BD^2 +BC^2 = 200^2, and since BC = BD x tan(25)/(tan15) this becomes 200^2 = (BD)^2 (1+ tan^2(25)/tan^2(15)). You can now solve for BD, and finally determine AB using length BD x tan (25).

[Yusf]

Hey! The answer is 46.47. It EXACTLY matches with the answer of the book. Thanks a lot to Ebaines and Wonder girl for helping me.