Hi,
I think there is a typo error in the expression to be
proved, as I obtained 289 sin 2(theta) + 240. Also, AB = 30 cm as
shown on the diagram but it is written as 3 cm in the problem
statement.
The approach:
1. angle ABE = angle CDB = theta (angles in the same
segment).
2. From triangle ABE: AE = 30 cos (theta), BE = 30 sin
(theta).
3. From triangle CDE: DE = 16 cos (theta), CE = 16 sin
(theta).
4. Area = area of triangle ABC + area of triangle ADC
= 1/2 (30 cos theta + 16 sin theta)(30 sin theta) +
1/2
(30 cos theta + 16 sin theta)(16 cos theta).
5. Expand and simplify to 289 sin 2(theta) + 240.
Thanks!
Cheers,
Wen Shih
Thanks wee_ws! My approach to this question was the same as
yours. But unfortunately, the only difficulties I have is "Expand
and simplify to 289 sin 2(theta) + 240.". I tried but I just can't
transform the equation to the above. That's what initially led me
to think that I might have done it incorrectly. Is there some way
to reduce it to 289 sin 2(theta) + 240.?
