Trigonometry: Right-angled triangle

[Brian Bart]

Hi Guys
I need help with this question
so if you can help me with the answer please please.

View attachment 9241

View attachment 9242

 

[skeeter]

part (i) of the student's response is correct.

part (ii) has an algebra error in determining the length of DC

if $DC^2 = DB^2 - CB^2$, then $DC \ne DB - CB$

the trig for part (iii) is correct ... can't say I agree with using 120 degrees for angle ADB since it induces rounding error in determining the length of AB.

Using the equation $\sin(40) = \dfrac{BC}{AB} \implies AB = \dfrac{BC}{\sin(40)}$ will not induce that error.