P3 Applied Trig

Hi,

just a quick one, need help with first part of question, rest seems ok:

ABCD represents a rectangular table with sides 3.5m and 1.5m. It has been turned so that it wedges in a passage of width 2.5m. Given that θ° is the acute angle between the longer side and the passge, show clearly why:

7sinθ° + 3cosθ° = 5

Cheers

Streety

Reply 1

dvs

If you draw the rectangle, let the angle the longer side makes be θ, and the angle the shorter side makes be 90-θ.
(http://rcode.net/rect.JPG)
sinθ = x/3.5
sin(90-θ ) = y/1.5, but sin(90-θ ) = cosθ
cosθ = y/1.5
x = 3.5sinθ
y = 1.5cosθ

x + y = the height of the passage = 2.5
3.5sinθ + 1.5cosθ = 2.5 [multiply by 2]
7sinθ + 3cosθ = 5

QED