The line AB is the line of intersection of the planes ABCD and ABEF. In order, to find the angle between the two planes. Draw a line XP in the plane ABEF which is perpendicular to AB also draw a line YP in the plane ABCD which is perpendicular 2 the line AB. Then the angle XPY gives us the angle between the planes.

The angle between a line and a plane.
Consider the line OE which meets the plane ABCD at point O.In order to get the angle between
the line OE and plane ABCD drop a perpendicular from E to the plane.The perpendicular meets
the plane at point F∴the projection of OE onto the plane is of .So the agnle between the line OE and plane ABCD
is EOF.
Example:
A rectangular box with top WXYZ and base ABCD.

AB = 6cm
BC = 8 cm
And WA = 3 cm
Calculate a) the length of AC
b) The angle between WC and AC

A VIDEO ABOUT THREE DIMENSIONAL GEOMETRY PROJECTION

A right pyramid VABCD stands on a square base of side 4cm. The slant edges are or 8cm. Calculate

Height of VO

the angle between a slant edge and the base

the angle between a sloping face and base

In a square based pyramid, V is vertically above the middle of the base, AB – 10cm and VC = 20cm. Find

AC

the height of the pyramid

the angle between VC and the abase ABCD

A point A is 200m due south of a tower a point B is due east of the tower and on a bearing of 037^{0} from A.

In the diagram, A, B and O are points in a horizontal plane and P is vertically above O where OP = (h) m. A is de west of O, B is due south of O and AB = 6m. The angle of elevation of P from A is 25^{0} and from B is 33^{0}.

Find the length of AO in terms of h.

Find the length of BO in terms of h

Find the value of h.

The angle of elevation of the top of a tower is 36^{0} from a point. A due south of it. The angle of elevation of the top of the tower from another point B, due east of the tower is 29^{0}. Find the height of the tower if the distance AB =50m

An observer at the top of at tower of height 15m sees a man due west of him at an angle of depression of 31^{0}. He see another man due south at an angle of depression of 17^{0}. Find the distance between the men.

4. The angle of elevation of the top of a tower is 270 from a point A due east it .The angle of elevation of the tower is 110 from another point B due south of the tower. Find the height of the tower if the distance AB = 40m.

## THREE DIMENSIONAL GEOMETRY PROJECTION:

Consider the diagram below;-

BD is the projection of BA on the line.

The angle between two planes.The line AB is the line of intersection of the planes ABCD and ABEF. In order, to find the angle between the two planes. Draw a line XP in the plane ABEF which is perpendicular to AB also draw a line YP in the plane ABCD which is perpendicular 2 the line AB. Then the angle XPY gives us the angle between the planes.

The angle between a line and a plane.

Consider the line OE which meets the plane ABCD at point O.In order to get the angle between

the line OE and plane ABCD drop a perpendicular from E to the plane.The perpendicular meets

the plane at point F∴the projection of OE onto the plane is of .So the agnle between the line OE and plane ABCD

is EOF.

Example:

A rectangular box with top WXYZ and base ABCD.

AB = 6cm

BC = 8 cm

And WA = 3 cm

Calculate a) the length of AC

b) The angle between WC and AC

A VIDEO ABOUT THREE DIMENSIONAL GEOMETRY PROJECTIONA point A is 200m due south of a tower a point B is due east of the tower and on a bearing of 037

^{0}from A.In the diagram, A, B and O are points in a horizontal plane and P is vertically above O where OP = (h) m. A is de west of O, B is due south of O and AB = 6m. The angle of elevation of P from A is 25

^{0}and from B is 33^{0}.^{0}from a point. A due south of it. The angle of elevation of the top of the tower from another point B, due east of the tower is 29^{0}. Find the height of the tower if the distance AB =50m^{0}. He see another man due south at an angle of depression of 17^{0}. Find the distance between the men.4. The angle of elevation of the top of a tower is 270 from a point A due east it .The angle of elevation of the tower is 110 from another point B due south of the tower. Find the height of the tower if the distance AB = 40m.

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