(e) We can simply use the cosine rule, as we have two sides and one angle to find one side.
BC² = 10² + 10² - 2(10)(10)cos(64)
BC² = 100 + 100 - 200cos(64)
BC² = 200 - 200cos(64)
BC² ≈ 112.3257706...
BC ≈ 10.59838... ≈ 10.6cm (1 dp)
(f) Since you're given the angle of β, you can use that to subtract that from the angle of α. Now, we know that the distance of the flight of the plane is parallel to the ground, because they are flying at a constant height.
Using alternate angles, you can refer to my diagram. Now, you need to find out what γ is, and you can do so by using the angle sum of a triangle. Since you have the angles of interest, you have to use the sine rule to find the length from Charmaine to the dotted line.
Now, you have every single element to using the cosine rule to find the diagonal. Once you find the diagonal, you'd have to use the cosine rule again to find the distance of the flight path.
Now, you have a distance and a time, and divide the distance by the time to find the speed in terms of kilometres, and you're done.
