Final answer:
By using geometric relations and the similarity of triangles, the height of the cliff is determined to be 180 meters high. This involves setting up a proportion between the known height and distance of a pole and the unknown height and distance of the cliff.
Step-by-step explanation:
The question relates to finding the height of a cliff using geometric principles and involves constructing a right-angled triangle. Let's call the height of the cliff H. We know the height of the pole is 20 m and the distances from the pole to the point where the line hits the ground and from that point to the base of the cliff are 15 m and 120 m respectively. By finding the similar triangles and applying Pythagoras' theorem, we can solve for H.
First, let's consider the triangle formed by the top of the pole, the base of the pole, and the point where the line from the top of the cliff hits the ground. We have a right-angled triangle here where the base (adjacent side of the triangle) is 15 m, and the height (opposite side of the triangle) is 20 m.
Now, extending this line to the base of the cliff, we have another similar right-angled triangle with the entire line as the hypotenuse that hits the ground at a distance (base of the larger triangle) of 15 m + 120 m = 135 m from the base of the cliff. Therefore, by the similarity of triangles, we can set up a proportion where 15/20 = 135/H. Solving this proportion gives us the height of the cliff, H = 180 m. Hence, the cliff is 180 m high.