Week 9 and 10 – Jss 3 Second Term Mathematics Notes

WEEK NINE
APPLICATION OF TRIGONOMETRIC RATIOS
Examples: a ladder of 10m is placed against a vertical wall such that the angle between the ladder and the horizontal ground is 30^o

1. Calculate the distance up the wall the ladder reaches

   Solution
                           Sin 30^o =
                           X = 10 x sin 30^o
                           X = 5m

 
 
 
 
 Exercise
In a circle, point O is the centre AB is a chord with length 16cm. The radius of the circle is 10cm calculate

1. The angle AÔB
2. The vertical line from the centre to the line AB

ANGLE OF ELEVATION AND DEPRESSION
Tangent ratio can be used to solve real life problems such as angles of elevation and depression.

1. Angle of Elevation
   

   Example: A tower AB is 50m high if the distance from the point C is 80m from A on a level ground find the angle of elevation of B from C

 
 
 Let be the angle of elevation of B from C, tan = = 0.6250
= tan^-1(0.6250) = 32^o

1. Angle of Depression
   

   Example: From the top of a cliff of 150m high, John observes that the angle of depression of a boat at sea is 20^o calculate the distance of the boat from the foot of the cliff (ignore John’s height)

Solution
                            Tan 20^o =
                            X =
                            X = 412m

 
 
 Exercise

1. The angle of elevation of the top of a building is 35^o from a point 55m away on a level ground. Calculate the height of the building
2. From the top of a mountain 150m high a girl notices that the angle of depression of an object at sea is 350^o. find the distance of the object from the foot of the mountain (ignore the height of the girl)

 Assignment

1. Calculate angle QRS
2. PR

 WEEK 10
BEARINGS
Bearings are measured from the north in the clock wise direction

 
 
 
 
 
 
     
 
 
Examples of bearings using three digits

1. The bearing of point A from B is 090^o

1. The bearing of point P from Q is 210^o

 
 
 
 Exercise
Point P and Q are respectively 30km North and 20km west of point R. Work out the bearing of Q from P.
Assignment
From point P Wisdom cycles 18km north to point Q, then east to point R. If the bearing of R from p is 065^o. What is the distance from Q to R.?