QR question with triangles and trig

[baywatch123]

---

Members don't see this ad.

The solution is given like so, but i've put some color coding and fillings to help clarify

we know the lower triangle is a 30-60-90 triangle. so the red line must be (x)sqrt(3)
we also the upper triangle is expressed by 5sin(theta)

equate. 5sin(theta) = (x)sqrt(3)

and they solved it etc etc. but basic trig has been pretty rusty and i'd like to know what the 5sin(theta) represents, i know it comes from the upper triangle but why couldn't they do 5cos(theta)

thanks

 

[shonster460]

So from the way the question is presented, theta would be the top angle. From this, sin(theta) = (x)sqrt(3)/5 because of opposite/hypotenuse. Simple algebra will tell you that 5sin(theta) represents that side that splits the quadrilateral (red).

sin(theta) = (x)sqrt(3)/5
5*sin(theta) = 5*[(x)sqrt(3)/5]
5*sin(theta) = (x)sqrt(3)

Hope this helps!

 

[baywatch123]

So from the way the question is presented, theta would be the top angle. From this, sin(theta) = (x)sqrt(3)/5 because of opposite/hypotenuse. Simple algebra will tell you that 5sin(theta) represents that side that splits the quadrilateral (red).

sin(theta) = (x)sqrt(3)/5
5*sin(theta) = 5*[(x)sqrt(3)/5]
5*sin(theta) = (x)sqrt(3)

Hope this helps!

yes it helps 100%... kinda mad that i couldn't see that.... it's such an easy example