# geometry

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ABCD is a trapezoid with DC parallel to AB, AB=4, AD=4, angle A=60, angle C=45. Find DC and BC

• geometry -

Make a sketch, marking all the given data

join BD
since AB = AD = 4, the triangle is isosceles, furthermore it is easy to see that it must be equilateral, all angles are 60° and BD = 4

By alternate angles , angle BDC = 60° leaving angle CBD = 75°
Using the sine law,
BC/sin60 = 4/sin45
BC = 4sin60/sin45 = 4.8989 or appr. 4.9

find DC in the same way

• Maths -

Find the radius of a right circular cyilender whose volume is 3080cu.cm and height is 20cm.

• geometry -

v = pi r^2 h
3080 = pi * 20 * r^2
r^2 = 3080/20pi
r = ...

• geometry -

The two triangles above are similar. If XZ = 10 cm, YZ = 15 cm, and AC = 18 cm, what is the length of BC?

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