Question

Help?
Triangle ABC has AC = BC, and ∠ACB = 96°. D is a point in triangle ABC such that ∠DAB = 18° and ∠DAB = 30°. What is the measure (in degrees) of ∠ACD?

Answer 1

anyone?

Answer 2

We know, by the 1800-Triangle Theorem, angle ADB = 132 degrees.

From addition addition, we also know:
angle CAD = 24 degrees
angle CBD = 12 degrees

It appears we have four unknowns, the angles labeled a, b, c, and d. We know
1) at vertex C
a + d = 96
2) In Triangle ACD
24 + a + b = 180
a + b = 156
3) In Triangle BCD
12 + c + d = 180
c + d = 168
4) at vertex D
132 + b + c = 360
b + c = 228

That's four unknowns and four equations, but the trouble is, those four equations are not independent: we get two different ways to get
a + b + c + d = 324

I believe we would need to use trigonometry. We could pick an arbitrary length for AB, and use the Law of Sines to find AC = BC, AD, and BD. From angle CAD, we could use the law of cosines to find length CD, and then use the Law of Sines or Cosines to solve for the angle. That would work, but it's a rather unsatisfying approach, because we would have to use an inverse trig function to give us the angle. There should be a way to do it with pure geometry, without having to use inverse trig functions.

From the software I used to create the diagram, I did find that the angle is 78 degrees. Of course,

Answer 3

what is there a way you can break down into steps?

Answer 4

Use the law of sines.

Answer 5

law of what?

Answer 6

how can angleDAB = 18 and 30?

Answer 7

I dont even know

Answer 8

is there a typo? :O

Answer 9

i wish i knew
ima make a educated guess been trying to figure this out forever

Answer 10

no apparently law of sines makes it possible but i dont know how it works

Answer 11

theres another problem with your directions.
you can't construct an isosceles triangle with base angle 96 degrees

Answer 12

this is an impossible triangle. the angle <ABC must equal to 96 degrees, and 96 + 96 is greater than 180

Answer 13

law of sines

Answer 14

but i dont know how to do law of sines

Answer 15

lets start with a diagram

Answer 16

looks someting like this

Answer 17

thanks ill just ask my teacher on monday i know the answer just dont know how to use the law

Answer 18

hmmm

Answer 19

ok