Question: From the top of a tower of height h meters the angle of depression of a red car is φ° and the angle of depression of a blue car which is on the opposite side of the tower is θ°. If the distance between the foot of the tower and the red car is y meters, then find the height of the tower and the distanc between the two cars. Assume that the points of location of the cars and the foot of the tower are collinear. [Given y = 115, θ = 55° and φ = 40°.]
A ) 96 m & 182 m B ) 98 m & 183 m C ) 96 m & 184 m D ) 101 m & 182 m
Steps to derive
5 Draw the figure from the given data.
6 Let A represent the top of the tower.
7 Let BC represents the distance between two cars.
8 Let h represents the height of the tower and x represents the distance between the foot of the tower and the blue car.
9 In right triangle ABD, tan 40° = ADBD = h115 Þ h = 115 tan 40° Þ h » 96 meters. [Substitute the value of tan 40° and simplify.]
10 In right triangle ADC, tan 55° = hx Þ tan 55° = 96y Þ y » 67 meters. [Substitute the value of tan 55° and simplify.]
11 So, the distance between the two cars, BC = 115 + y = 115 + 67 = 182 meters.
