Question

Two hunters A and B of e same height of 1.6 tall were standing on a horizontal plane at the opposite direction. The hunters sighted a bird on top of
a coconut tree of height 8m standing between them, The angle of elevation of the two hunters A and B are 30 degree and 60 degree respectively 1(a)Sketch a diagram to illustrate this information. 1(b)Which of the two hunters
Is closer to the coconut tree.

Answer 1

Answer on Question #80013 – Math – Trigonometry

Question

Two hunters A and B of the same height of 1.6 tall were standing on a horizontal plane at the opposite direction.

The hunters sighted a bird on top of a coconut tree of height 8m standing between them.

The angle of elevation of the two hunters A and B are 30 degree and 60 degree respectively.

1 (a) Sketch a diagram to illustrate this information.

1 (b) Which of the two hunters is closer to the coconut tree?

Solution

1 (a)

Horizontal line

$l_{1}$ - height hunter A

$l_{2}$ - height hunter B

$d_{1}$ - distance between hunter A and coconut tree

$d_{2}$ - distance between hunter B and coconut tree

H – height of coconut tree

α - angle of elevation hunter A

β – angle of elevation hunter B

$$I_1 = 1.6 \, \text{m}$$ $$I_2 = 1.6 \, \text{m}$$ $$H = 8 \, \text{m}$$ $$\alpha = 30{}^\circ$$ $$\beta = 60{}^\circ$$

Solution

1(b)

$$\tan(\alpha) = \frac{(H - l_1)}{d_1}$$ $$d_1 = \frac{(H - l_1)}{\tan(\alpha)}$$ $$d_1 = \frac{(8 - 1.6)}{0.57735} = 11.085$$ $$\tan(\beta) = \frac{(H - l_2)}{d_2}$$ $$d_2 = \frac{(H - l_2)}{\tan(\beta)}$$ $$d_2 = \frac{(8 - 1.6)}{1.73205} = 3.695$$

Because $d_2 < d_1$, the hunter B is closer to the coconut tree.

**Answer**: the hunter B is closer to the coconut tree.

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