6. Five mark example problems II

1. A TV tower stands vertically on a bank of a canal. The tower is watched from a point on the other bank directly opposite to it. The angle of elevation of the top of the tower is \(58^{\circ}\). From another point \(20 \ m\) away from this point on the line joining this point to the foot of the tower, the angle of elevation of the top of the tower is \(30^{\circ}\). Find the height of the tower and the width of the canal. (Use \(tan \ 58^{\circ} = 1.6003\))

 

 

The height of the tower \(=\)  

 

The width of the canal \(=\)  

 

(Note: Enter the number in the first box and the unit (short form)  in the second box. Round off the answers to \(2\) decimal places.)

 

2. Two trees are standing on flat ground. The angle of elevation of the top of both the trees from a point \(X\) on the ground is \(40^{\circ}\). If the horizontal distance between \(X\) and the smaller tree is \(8 \ m\) and the distance of the top of the two trees is \(20 \ m\), calculate:

 

Answer:

 

(i) The distance between the point \(X\) and the top of the smaller tree \(=\)

 

(ii) The horizontal distance between the two trees \(=\)  

 

(Use: \(cos \ 40^{\circ} = 0.7660\))