The question is related to trigonometry and we have to use the formula of double angle .
Here we use double angle formula of tangent function which is
Given expression is
Comparing it with double angle formula, we will get x = 5
SO the required expression is equal to
So the answer is tan(10) .
Answer:
The volume of the observatory is 497.43
Step-by-step explanation:
i) The diameter of the floor is 10 feet. The floor is circular and has a radius,
r = = 5 feet.
Therefore the area of the circular floor of the observatory
= = 3.14159 ×
= 78.54
ii) The observatory is made up of two parts
a) 3 foot tall cylinder
∴ volume of cylinder = × h
= 78.54 × 3
= 235.62
b) hemisphere = ×
= 0.6667 × 78.54 × 5 = 261.81
c) Therefore the total volume of the observatory is = a) + b)
= 235.62 + 261.81 = 497.43