C4 Trigonometry Question

Hi

The question is : A table is jammed in a corridor. The table is 120 cm long, and 80 cm wide, and the width of the corridor is 130 cm.

Show that 12 sin (theta) + 8 cos (theta) =13

Reply 1

calcium878

At first thoughts, this is gonna come from sin^2(theta) + cos^2(theta) = 1, then replace a sin(theta) and a cos(theta) by right-angled trig values. (eg sin(theta) = opposite/hypotenuse). Draw yourself a diagram if there isn't one already.

Reply 2

EvenStevens

I think I did it very crudely <_<

I got

12sin\theta + 8cos\theta = 13.3

Just by finding the hypotenuse of the table...

Yeah, I think I did it wrong.

Reply 3

The Great Khali

Heres the diagram from the book. I know how to find the angle but not the equation

Reply 4

username62978

Draw straight lines at each vertex, perpendicular to the corridor, so that it looks like a tipped rectangle in a box.

There will now be four triangles surrounding the table. Mark in which of the angles are equal to theta (using sum of angles on a straight line, z angles, etc.), and see if you can work out any more of the sides of the triangles (in terms of theta) using basic trig.

Spoiler

Reply 5

Cartesian_

draw lines perpendicular to the hall walls against the corners of the table.
find the angles that equal theta and then take the unknown lengths to be X and 130-X

you can know for equations and rearrange them to equal x

Reply 6

The Great Khali

Thanks for the help guys, i thought everyone forgot about this thread until I recieved an e-mail today :biggrin:

Reply 7

azqw204

Sorry to dig up an old thread, but does anyone know the answer as to how to work this out coz I have no idea

Reply 8

EEngWillow

Basically read the thread. Other posters have covered it pretty well.

Reply 9

azqw204

Original post by EEngWillow

Basically read the thread. Other posters have covered it pretty well.

they havnt tho, one has sed their answer is wrong and i dont understand the other one....
any help please????!!!? :frown:

Reply 10

EEngWillow

Original post by azqw204

they havnt tho, one has sed their answer is wrong and i dont understand the other one....
any help please????!!!? :frown:

Read post #5. If it still doesn't make sense, give us a more detailed explanation of what doesn't make sense. We avoid giving out full solutions, so without more information on which part you don't understand we can't actually help you.