Height of tower AB is 30 m where B is foot of tower. Angle of elevation from a point C on level ground to top of tower is 60° and angle of elevation of A from a point D x m above C is 15° then find the area of quadrilateral ABCD.
Height of tower AB is 30 m where B is foot of tower. Angle of elevation from a point C on level ground to top of tower is 60° and angle of elevation of A from a point D x m above C is 15° then find the area of quadrilateral ABCD.
- 300(\(\sqrt{3}\)-1)
- 600(\(\sqrt{3}\)-1)
- 150(\(\sqrt{3}\)-1)
- 100(\(\sqrt{3}\)-1)
The Correct Option is B
Solution and Explanation
tan 60° = \(\frac{30}{y}\) = \(\sqrt{3}\)
\(\Rightarrow\) y = 10\(\sqrt{3}\)
tan 15° = \(\frac{30-x}{y}\)
(2 - \(\sqrt{3}\))10\(\sqrt{3}\) = 30-x
x = 30-20\(\sqrt{3}\) + 30
x = 60-20\(\sqrt{3}\)
Area of ABCD = xy =(60-2\(\sqrt{3}\)).10\(\sqrt{3}\)
= 600(\(\sqrt{3}\)-1)
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Concepts Used:
Range
The range in statistics for a provided data set is the difference between the highest and lowest values. For instance, if the provided data set is {2,5,8,10,3}, then the range will be 10 – 2 = 8.
Thus, the range could also be described as the difference between the highest observation and lowest observation. The acquired result is called the range of observation. The range in statistics states the spread of observations.
