## nath 3 years ago Find the measure of angle phi in degrees and the length of segment x in centimeters.

1. Directrix

Diagram?

2. nath

SRRY I HAV AM DRAWING IT

3. nath

|dw:1327994270675:dw|

4. Directrix

If the dashed segment is an altitude or an angle bisector of the equilateral triangle, the "mystery" angle has measure 30.

5. nath

|dw:1327994428232:dw| HERES A BETTER PICTURE

6. atjari

theta is 30 degrees and x=7cm

7. nath

CAN YOU PLEASE EXPLAIN HOW YOU CAME UP WITH THESE VALUES

8. Directrix

What are you given about the dashed segment? Then, I can tell you.

9. nath

Dividing an equilateral triangle in half leads to the next special triangle that we will look at. Consider the figure showing an equilateral triangle with a line dividing it down the middle. This line divides both the angle at the top of the triangle and the base of the triangle into two equal parts.

10. Directrix

@ nath, how do you know that the equilateral triangle has been "halved?"

11. nath

it was given with the question

12. Directrix

@Cyno How do you know "since that angle is cut directly in half to ..?" Where is it given?

13. atjari

cos60=x/14 1/2=x/14 x=7 90+60+theta=180 theta=30

14. nath

thank you

15. Directrix

|dw:1327994931350:dw|

16. atjari

yw

17. Directrix

Trig is not required. Use the 30-60-90 Theorem. b = 7 times square root 3.

18. nath

for some reason that isnt the answer

19. Directrix

@ Nath 7 times square root 3

20. nath

x =7

21. Directrix

7 times square root(3) = 12.1243557

22. nath

i got that but the answer for x is x=7

23. Directrix

x=7. 7times square root 3 is the length of the altitude (dashed segment on drawing which everyone but me knows intersects at a right angle :))

24. nath

i still do not understand how x=7 still . after we found that the value is about 12 how do we go from 12 to 7

25. atjari

c=14 so c^2=14^2

26. nath

so is this what you all mean b^2+ (7)^2=(14)^2

27. nath

right but atjari said c=14 thats why im confused.. you said c^2=14