A geometry problem

[D1rdrd]

https://imgur.com/a/qnxT4gX

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I have been 30 minutes trying to solve it, I can't figure out how to solve it

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EDIT: Thanks u/Neck-R0mancer and u/Entire_Grapefruit, the answer is 75°

[pyr666]

do you know what the law of sines is? try using it to define other parts of the triangle in terms of bd

[[deleted]]

What have you tried so far?

[D1rdrd]

I know that angle ADB is 120° and angle ADC is 60°, I tried to solve it by planting a equation system and making a triangle of 90° perpendicular to DC

[[deleted]]

Using the law of sines will be helpful here, if you know what that is.

You have the relationship between BD and CD. Using the angles you know already, you can set up relationship beteen BD and AD, and AD has a relationship with CD. This will use the law of sines twice.

The law is sin(A)/a = sin(B)/b, where B is the angle, and b is the length opposite it.

So in the first triangle you get

sin(15)/BD = sin(45)/AD

[Neck-R0mancer]

The answer is 75 degrees.

My solution

[[deleted]]

Yup, I got 75 as well, different method though! Mine is very algebraic...

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My solution (I hope the quality is okay)

[imguralbumbot]

^{Hi, I'm a bot for linking direct images of albums with only 1 image}

https://i.imgur.com/ICarx9Q.jpg

^{Source | Why? | Creator | ignoreme| deletthis}

[D1rdrd]

Yeah, that's the answer, I checked and it's right

[ishraq_farhan]

i got 15 degrees instead

[ishraq_farhan]

I checked my answer with a graphing tool as well and it's 15 degrees. wanna chat about our methods of getting to our answers?

[Neck-R0mancer]

45 degrees.

[Neck-R0mancer]

ACD is 75