Example:

A man who is 2 m tall stands on horizontal ground 30 m from a tree. The angle of elevation of the top of the tree from his eyes is 28˚. Estimate the height of the tree.

Solution:

Let the height of the tree be h. Sketch a diagram to represent the situation.

tan 26˚ =

h – 2 = 20 tan 26˚

tan 26˚ = 1.179

h = (20 ´ 1.179) + 2

h = 23.58 + 2

= 25.58

The height of the tree is approximately 25.58 m.

Bearing and Distances of Places Strictly by Application of Trigonometric Ratios

ASSESSMENT

1. Sin(A+45°)sin(A-45°) =
   (a) −1/2cos(2A)
   (b) −1/2sin(2A)
   (c) 1/2cos(2A)
   (d) one of Above
2. Sin5θcos2θ =
   (a) 1/2[sin7θ+sin3θ]
   (b) [sin7θ+sin3θ]
   (c) 1/2[sin7θ-sin3θ]
   (d) None of Above
3. 2sin12°sin46° =
   (a) cos34°cos58°
   (b) sin34°+sin58°
   (c) sin34°-sin58°
   (d) cos34°-cos58°
4. (cos(x)-cos3x)/(sin3x-sin(x)) =
   (a) cot2x
   (b) tan2x
   (c) csc2x
   (d) sec2x

2sin(x+45°)sin(x-45°) =
(a) cos2x
(b) −cos2x
(c) sin2x
(d) −sin2x