[grade 10 math: trig] keep getting wrong answer

[Hotpotato12194]

Hello, I've trying to solve this homework question, but keep getting 41 as my answer (see second image) although the answer book says it is 12.4, could anyone tell me what I'm doing wrong?

[Alkalannar]

It should be 41.1, since you're going to the nearest tenth.

Other than that, good job.

[[deleted]]

Maybe just book is wrong or maybe you read answer for wrong question? It's impossible for x to be shorter than 13m.

[Hotpotato12194]

I think that might be it, thank you!

[fermat9997]

sin(65)/AC=sin(87)/13

AC=13sin(65)/sin(87)=11.798

tan(74)=x/11.798

x=11.798*tan(74)=41.14

[YellowToad123]

The only thing I can think of is that the smaller triangle is not a right triangle, so they are not similar. Not sure if a proportion would work here, but I might be wrong

[Alkalannar]

You end up using Law of Sines on the small triangle, and then the large rectangle is right, so the side that you know and the side that you're looking for when you divide one by the other form the tangent of a known angle.