Easy trigonometry question (1 Viewer)

[girlworld_club]

A rhombus has one diagonal 12cm long and the diagonal makes an angle of 28degrees23minutes with the side of the wall.

a) Find the length of the side of the rhombus.
b)Find the length of the other diagonal.

 

[Sy123]

Assuming that the angle that it makes with the "wall" is the angle of the intersection of the diagonal and the side.

I will put up a diagram later, but for now, since it is a rhombus, the diagonal cuts the rhombus into two isosceles triangles.
(Two sides are equal [Property of a Rhombus])
Therefore, the other angle in this triangle that is NOT obtuse, is equal to 28 degrees 22 minutes
Therefore the obtuse angle in this triangle is: 180 - 2 * (28degrees 22 mintues) [Angle Sum Of Triangle] = 123.3333

Using sine rule, where x is the diagonal

x/sin(23.38) = 12/sin(123.33)
Then do cross multiplication and you have x (the diagonal length)

Ill do b) later even though its really easy, I have to go right now

 

[girlworld_club]

there is a easier way of doing this. This appeared in my 2 unit book, way before we are introduced to the sine rule.

 

[barbernator]

all you need to do is simple trig.

For the first one, the answer is 6/cos(the angle)

the second one, 2x6tan(the angle)

 

[kazemagic]

You need to know the properties of the rhombus lol
I might have misinterpreted the question wrong tho. BTW in the above, when i wrote length, I meant the other diagonal length lol