From the top of a building 10m high, the angle of elevation of a fruit on top of a tree 25m is 30º. Calculate the horizontal distance between the building and the tree.
A
15\(\sqrt{3}\)m
B
5\(\sqrt{3}\)m
C
25\(\sqrt{3}\)m
D
30\(\sqrt{3}\)m
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
From the diagram above:
Tan 30º = \(\frac{15}{x}\)
\(\frac{\sqrt{3}}{3}\) = \(\frac{15}{x}\)
x\(\sqrt{3}\) = 3 x 15 = 45
x = \(\frac{45\sqrt{3}}{3}\) = 15\(\sqrt{3}\)m ( this is after rationalizing the denominator)
Source: WAEC / JAMB / NECO Classroom Archive (Record #70205)