Can someone please help me???
A line from the top of a cliff to the ground passes just over the top of a pole 6.0 feet high
and meets the ground at a point 7.0 feet from the base of the pole. If the point is 99 feet
from the base of the cliff, how high is the cliff to the nearest foot?
6:7::h:99
or
6/7=h/99
solve for h.
To solve this problem, we can use similar triangles and the concept of proportions.
Let's call the height of the cliff "h".
From the given information, we know that the distance from the base of the pole to the point where the line meets the ground is 7.0 feet. Additionally, we know that the distance from the base of the cliff to the same point is 99 feet.
Now, let's consider the two triangles involved: the larger triangle formed by the line from the top of the cliff to the ground, and the smaller triangle formed by the pole, the ground, and the point where the line meets the ground.
Since the two triangles are similar, we can set up a proportion:
height of cliff / distance from base of cliff = height of pole / distance from base of pole
Using the given values, we can plug them into the proportion:
h / 99 = 6 / 7
To solve for h, we can cross-multiply and then divide:
h * 7 = 99 * 6
h = (99 * 6) / 7
Now, let's calculate the height of the cliff:
h = 594 / 7
h ≈ 84.857 feet
Therefore, the height of the cliff is approximately 85 feet to the nearest foot.