A bird flies from a tree P on a bearing of N60º E to a building, Q, a distance of 200 km. It then changes course and flies to another tree R on a bearing of S30ºE. Tree R is directly east of tree P. Calculate the distance of the building to tree R.
A
200\(\sqrt{3}\)
B
100\(\sqrt{3}\)
C
100
D
\(\frac{200}{\sqrt{3}}\)
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
Tan \(\theta\) = \(\frac{\text{0pp}}{\text{Adj}}\)
Tan \(\theta\) = \(\frac{200}{\text{x}}\)
x = \(\frac{200}{\text{tan} 60}\)
x = \(\frac{200}{\sqrt{3}}\)
Source: Myschool Past Questions Archive (Record #74202)