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The diagram below represents a person standing at point A on top of building $AB$ which is 50 metres high. He observes 2 buses, C and D, that are on the same horizontal plane as B. The angle of elevation of A from C is $55^{\circ}$ and the angle of elevation of A from D is $55^{\circ}$ . $C\hat{A}D$ 1. Calculate the length AC to the nearest metre.
2. Calculate the distance (to the nearest metre) between two buses.
3. If the area of $\triangle{BDC}$ is $563 \text{m}^2$, calculate the size of $B\hat{D}C$
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## 1 Answer

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1. using sine rule,

sin55 = 50/AC

AC = 50/sin55

= 61 m

2. using cosine rule,

DC^2 = AC^2 + AD^2 - 2AC.ADcos65
DC^2 = (61)^2 +  (61)^2 -  2(61)(61)cos65
DC = 66 m

3. using pythagoras,

BD = sqroot(61^2 - 50^2)

= 35 m

sinBDC = 563/0.5(35)(66)

BDC = 29.17 degrees
by Diamond (43,708 points)

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