8. Five mark example problems IV

1. From the top of a \(12 \ m\) high building, the angle of elevation of the top of a cable tower is \(60^{\circ}\) and the angle of depression of its foot is \(30^{\circ}\). Determine the height of the tower.

 

Answer:

 

The height of the tower \(=\)  .

 

(Note: Enter the number in the first box and the unit (short form) in the second box.)

 

2. From a window (\(h\) metres high above the ground) of a house in a street, the angles of elevation and depression of the top and the foot of another house on the opposite side of the street are \(\theta_1\) and \(\theta_2\) respectively. Show that the height of the opposite house is \(h\left(1 + \frac{cot \ \theta_2}{cot \ \theta_1}\right)\).