chriszorr's GMA Questions

[Drunk]

Alright I decided to make one thread for my questions instead of a new one each time.
So, this time, how would I work out the height of the lighthouse in this diagram using the sine rule?



Thanks!

[jane1234]

180-46.2 = 133.8 (supplementary angles)

... 133.8 degrees is the second interior angle of the first triangle (with base 34m)

... the angle at the top of the first triangle is 18.6 degrees (by knowing that angles of a triangle add up to 180).

Thus we can use the sine rule: 34/sin(18.6) = x/sin(27.6) so solve for x (the line separating the two triangles).

Once that length is found, we can solve sin(46.2) = h/x for h and that will give the height of the lighthouse.

Hope that helps

[Drunk]

Oh okay thanks
Another one:

[IMG]http://img683.imageshack.us/img683/7582/unledlhl.png[/img]

Uploaded with ImageShack.us

Find the area of the shaded bit? The 5cm thing at the bottom is the distance between the centres of the circles btw.

[kamil9876]

Call the Centres A and B and the intersections C and D.

Consider the two triangles ABD and ABC. They have sidelengths 3,4,5 (exactly the same). Which happens to be a right angle triangle (by the converse of pythagoras), hence the area is 0.5*3*4=12. So 24 is the total area of the two triangles. Now you can find the area of the two sectors ABD and ABC. The sum of these two areas minus 24 gives the area of the black region (why? because that is the intersection of the two sectors and hence we have double counted that area when taking the sum of the areas of the two sectors).

[Drunk]

haha thanks, that was a bummer question tbh
Alright:

Two wheels (pulleys) have radii of length 15 cm and 25 cm and have their centres 60 cm
apart. What is the length of the belt required to pass tightly around the pulleys without
crossing?

[brightsky]

similar technique to the above. find the angle of the two sectors (using trig), and hence find the part of the circumference of each circle that you need to subtract (from the total circumference of the two circles).

[pi]

Two wheels (pulleys) have radii of length 15 cm and 25 cm and have their centres 60 cm
apart. What is the length of the belt required to pass tightly around the pulleys without
crossing?

There are some pretty funky general formulas for this on General Maths Dimensions (Ian Bull) if you want more challenges on pulleys

[monkeywantsabanana]

haha thanks, that was a bummer question tbh
Alright:

Two wheels (pulleys) have radii of length 15 cm and 25 cm and have their centres 60 cm
apart. What is the length of the belt required to pass tightly around the pulleys without
crossing?

I hope this helps - attachment.

[Drunk]

Thanks

1. A sphere of radius length 8 cm rests on the top of a hollow inverted cone of height 15 cm
whose vertical angle is 60◦. Find the height of the centre of the sphere above the vertex of
the cone.

2. Two circles intersect at A and B and, from any point P on AB produced tangents PQ and PR
are drawn to the circles. Prove that PQ = PR.

3. If AB is a chord of a circle with centre O and P is a point on AB such that BP = 4PA,
OP = 5 cm and the radius of the circle is 7 cm, find AB.