Hello, Please advise if I have worked this lot out correctly.

I have included a diagram to help explain what I am trying to do.

Looking at the kite I require to find the length of the side BC. Apart from the angles included the only other information I was given is the length of the diagonal, which is 40cm

I used the following idea

a / sinA = b / sinB

a / sin 25 = 40 / sin 100

a = 40 sin 25 / sin 100

a = 16.90 / 0.985 = 17.2 cm (3 sf)

BC = 17.2 cm. This is the hypotenuse of the right hand lower triangle in the kite.

I was asked to add a second diagonal BD and label the intersection. I know what an intersection is, but what do they mean by asking label it?

Do they mean; ABD?

I am required to find the length of the diagonal BD.

This is what I did.

I used the sin rule because when I look at the lower right hand side triangle, it is a right angle triangle and I have the angle opposite, so

sin 50 x 17.2 = 13cm

so the opposite side of the triangle length is 13cm

I then used pythagoras to find the length of the adjacent side

c = square root a^" - b^2

17.2^2 - 13^2 = 11.3 cm

Because I am asked for the length BD I have doubled it to 22.5 (3 sf)

Please advise if I have worked it out OK

Thanks

David