If the length of the shadow of a tower is increasing, then the angle of elevation of the sun is also increasing.
False.
Step 1: Suppose the height of the tower is \(h\) metres (a fixed value). Let the length of the shadow on the ground be \(d\) metres.
Step 2: In a right-angled triangle, the angle of elevation \(\theta\) of the sun is given by:
\[ \tan \theta = \dfrac{\text{Opposite side}}{\text{Adjacent side}} = \dfrac{h}{d} \]
Step 3: Since the tower’s height \(h\) is constant, the only changing quantity is the shadow length \(d\).
Step 4: If the shadow becomes longer (\(d\) increases in metres), the fraction \(\dfrac{h}{d}\) becomes smaller.
Step 5: When \(\tan \theta\) decreases, the angle \(\theta\) (angle of elevation of the sun) also decreases.
Step 6: Therefore, as the shadow length increases, the angle of elevation of the sun decreases, not increases.