christinaxxx 4 years ago how do u use trigonometry to determine an angle of an isosceles triangle??

1. ash2326

Supposedly we are given the sides of isosceles triangle. If we draw a perpendicular from the vertex to the third side (two other sides are equal). It'll bisect the third side. |dw:1331409664200:dw|

2. ash2326

We need to find the two angles x and the third angle y we know $\cos \theta= \frac{base}{hypotenuse}$ here $\cos x= \frac{b/2}{a}$ from this we can find x and y=180-2x

3. amistre64

angles are determined by undoing a ratio

4. amistre64

trig(angle) = ratio angle = arctrig(ratio)

5. amistre64

which angle are you interested in finding?

6. christinaxxx

both of them

7. amistre64

there are 3 angles in a triangle :) I assume you mean the base angles?

8. christinaxxx

yup! sorry bout that

9. amistre64

in order to determine the solution to any triangle we need a few bits of information to deduce the unknowns with

10. amistre64

do you have a particular example we can work on?

11. christinaxxx

unfortunately...no :( its a studyguide for finals and i'm reviewing

12. amistre64

well, there are 2 "laws" that can be used when we have certain information; one is the law of sines and the other is a more adaptable form of the pythag thrm

13. amistre64

law of sines equates angles with the length of the side opposite the angle $\frac{sin(C)}{c}=\frac{sin(B)}{b}=\frac{sin(C)}{c}$ |dw:1331413584401:dw|

14. amistre64

the law of cosines is the more general form of the pythag thrm: $c^2=a^2+b^2-2ab\ cos(C)$

15. amistre64

when the angle C is 90 degrees; that simply reverts the the usual: c^2=a^2+b^2

16. amistre64

the law of cosines is good for determing the length of sides; and the law of sines is easier to implement once you know the ratio of angles and sides