In triangle PQR, PQ = 15 cm, PR = 10 cm and angle PQR = 40 degrees

i) Show that sin R = 0.9642 to 4 d.p.

ii) Illustrate on a sketch the two possible configurations of triangle PQR.

iii) Find the area of the smaller triangle PQR.

I seriously dont even know how to do (i)!

2. First, use the law of sines:

$\frac{L(PR)}{\sin Q} = \frac{L(PQ)}{\sin R}$

Now, the fact that $\sin R = 0.9642$ means that R is an angle whose measure is very close to 90 degrees. But you can't tell from the given information whether that angle is greater or less than 90 degrees, since there are two angles that have that value for the sine.

The triangle with the smaller area has the larger angle R. Do you know why?

3. yep (cause it'll mean the angle used to find the area of the triangle - P - will be smaller and thus the area and triangle in general will be smaller)

thanx