(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.
Explanation
(a)
Length of arc AB = (frac{108°}{360°} times 2 times frac{22}{7} times 7 = frac{132}{10} =13.2cm)
Perimeter of the sector = (13.2cm + 7cm + 7cm = 27.2cm)
(b)
Let T = top of cliff, C = bottom of cliff, B = the boat.
Since angle of depression = 30°
then < CBT = 30° (alternate angles TR//CB)
(therefore text{Height of the cliff} (CT) = 120 times 0.5774m)
= (69.288m approxeq 69.3m)