Question

First person to solve gets fan, and help in another subject.

Answer 1

Um let's see.

Answer 2

You can solve for angle D

Answer 3

Where an angle \(A\) is opposite to a side \(a\) of a triangle, (the other sides are \(b,c\))
the cosine rule says
\[a^2=b^2+c^2-2bc\cos(A)\]

Answer 4

^that too. Wow I can't believe I didn't see that...

Answer 5

use \(A=\theta\)
and the solve an equation for each triangle for \(\cos(A)\), then equate these

Answer 6

I don't know how

Answer 7

\[4.1^2=6.8^2+\overline{AD}^2-2(6.8)(\overline{AD})\cos\theta\]

Answer 8

What do you get for the other triangle?

Answer 9

Can you simplify the eqation anymore so I can solve it? I don't get that.

Answer 10

We have (two triangles) two equations, and two unknowns BD and AD.

We cannot solve one equation at a time, we need to solve them simultaneously.

Answer 11

Please help me:((

Answer 12

This problem is more challenging than most because of the number of calculations involved. At least that's my take on it. Earlier (when you first posted this question) I suggested applying the Law of Cosines. If you follow that advice you will have to find ways to eliminate some of the variables.

Before we move any further on: Double check the instructions. Do the instructions say anything about the triangle being isosceles?

Unfortunately, I need to get off the Internet now. I'll be back on again in the morning.

Note that you will probably get more responoses if you become involved, sharing your thoughts, your first efforts, and so on. You have to be involved to learn this material.

Answer 13

"Can you simplify the eqation anymore so I can solve it? I don't get that.." I encourage you to look for ways to eliminate one or more of the unknown quantities. I was able to eliminate all but side AD.