MHB Math Struggles: My Little Bro's Story

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The discussion revolves around a math problem related to trigonometry that the user's younger brother is struggling with. The thread was redirected to the Trigonometry subforum for better assistance. Key points include the application of the law of sines to solve for sides in a triangle and the use of cosine to find a specific segment length. The user seeks help in understanding these concepts to better assist their brother. Overall, the focus is on clarifying trigonometric principles for problem-solving.
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hi guys my little bro came to me with this as he's doing a maths course like me but he wanted me to help but could with some but not this bit hahah

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Re: spot the issue

I have moved this thread here to our Trigonometry subforum, as it is a better fit for the questions.
 
Re: spot the issue

For (i), the law of sines says that
\[
\frac{AB}{\sin48}=\frac{BC}{\sin40}=\frac{23}{\sin40}
\]
For (ii), $AD=AB\cos40$.
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...

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