(a) The angle of a sector of a circle radius 7cm is 108°. Calculate the perimeter of the sector. [Take \(\pi = \frac{22}{7}\)] (b) A boat is on the same hor...
Question 1 Report
(a) The angle of a sector of a circle radius 7cm is 108°. Calculate the perimeter of the sector. [Take \(\pi = \frac{22}{7}\)]
(b) A boat is on the same horizontal level as the foot of a cliff, and the angle of depression of the boat from the top of the cliff is 30°. If the boat is 120m away from the foot of the cliff, find the height of the cliff correct to three significant figures.
Answer Details
(a) Radius \(r=7\text{ cm}\), angle \(=108^{\circ}\). Arc length \[=\frac{108}{360}\times2\pi r=\frac{108}{360}\times2\times\frac{22}{7}\times7=\frac{3}{10}\times44=13.2\text{ cm}.\] Perimeter of sector \(=\) arc \(+2r=13.2+14=\) 27.2 cm.
(b) Angle of depression \(=30^{\circ}\) equals the angle of elevation of the cliff top from the boat. With the boat \(120\text{ m}\) from the foot: \[\tan30^{\circ}=\frac{h}{120}\Rightarrow h=120\tan30^{\circ}=120\times0.5774=69.28\text{ m}\approx69.3\text{ m}.\]
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