A 15 m tower casts a 24 m shadow. At the same time a telephone pole casts a 16 m shadow. Find the pole’s height.
10 m
Step 1: When the Sun shines, tall objects like towers and poles form shadows on the ground.
Step 2: At the same time of the day, the angle of sunlight is the same. So, the tower and the pole will form similar right-angled triangles with their heights and shadows.
Step 3: For similar triangles, the ratio of height to shadow length will be equal.
That means:
\(\dfrac{\text{Height of tower}}{\text{Shadow of tower}} = \dfrac{\text{Height of pole}}{\text{Shadow of pole}}\)
Step 4: Substitute the known values:
\(\dfrac{15}{24} = \dfrac{h}{16}\)
Step 5: Solve for \(h\):
\(h = \dfrac{15}{24} \times 16\)
\(h = 10\)
Step 6: Therefore, the height of the pole is 10 m.