Check my work..?

Question

Check my work..?

anonymous · Answer

Check|dw:1419864118167:dw|

igreen · Answer

Question:

Two ropes, AD and BD, are tied to a peg on the ground at point D. The other ends of the ropes are tied to points A and B on a flagpole, as shown below:

Angle ADC measures 60° and angle BDC measures 45°. What is the distance between the points A and B on the flagpole?

misty1212 · Answer

$$\huge \color{red}\checkmark$$

misty1212 · Answer

i guess the best bet is to find $\overline{AC}$ then then subtract $\overline{BC}$

igreen · Answer

Here's my work:

First I find the measure of AC:

$\sf tan(60^o) = \dfrac{x}{9}$

Simplify tangent of 60 degrees:

$\sf 1.73205081 = \dfrac{x}{9}$

Multiply 9 to both sides:

$\sf x \approx 15.5884573$

Now I find the measure of BC.

$\sf tan(45^o) = \dfrac{x}{9}$

Simplify tangent of 45 degrees:

$\sf 1 = \dfrac{x}{9}$

Multiply 9 to both sides:

$\sf x = 9$

Therefore to find the length of AB, I will subtract the measure of BC from the measure of AC.

$\sf 15.5884573 - 9 \approx 6.59$

misty1212 · Answer

ok, the answer looks reasonable so i suppose the method is right
i typed in 
$$9(\tan(60)-\tan(45))$$ and got the same answer

igreen · Answer

Okay..but I was kind of confused on which angle $\sf 60^o$ was representing..

misty1212 · Answer

probably if i was smarter i would have typed in 
$$9\tan(60)-9$$

misty1212 · Answer

it has to be the entire angle

igreen · Answer

Yeah, I thought it could also be the angle between the hypotenuse of triangle ADC and triangle BDC.

misty1212 · Answer

if it was just the upper part then the angle would be $105$ which is not possible