Trigonometry 2

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.