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CONTENT

(c) Application of trigonometric ratios (angle of elevation and depression; bearing).

(d) Trigonometric ratios related to the unit circle.

(e) Graphs of sines and cosines.

Application of trigonometric ratios (angle of elevation and depression; bearing).

Angle of elevation:

Example 1:

The angle of elevation of a point P on a tower from a point Q on the horizontal ground is 600. If /PQ/=74m, how high is P above the ground?

Solution:

The relevant sides to 600 are Opp and Hyp (SOH)

$$Sin 60^o = \frac{x}{74} \\ \frac{\sqrt{3}}{2} = \frac{x}{74} \\ x = \frac{74\sqrt{3}}{2} \\ ∴ x = 37\sqrt{3}m$$

Example 2:

A man 1.8m tall observes a bird on top of a tree. If the man is 21m away from the tree and his angle of sighting the bird is 300, calculate the height of the tree.

Solution:

$$Tan 30^o = \frac{k}{21} \\ k = 21 tan 30^o \\ k = 12.12m$$

Thus height of the tree $$= k + 1.8m \\ = 12.12m + 1.8m = 13.92m$$

Angle of depression:

Example 3:

A boat can be sighted at the sea 71.5m from the foot of a cliff which is 26m high.

Lesson tags: General Mathematics Lesson Notes, General Mathematics Objective Questions, SS1 General Mathematics, SS1 General Mathematics Evaluation Questions, SS1 General Mathematics Evaluation Questions Third Term, SS1 General Mathematics Objective Questions, SS1 General Mathematics Objective Questions Third Term, SS1 General Mathematics Third Term
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