A telephone pole is supported by a steel cable which extends from the top of the pole to a point on the ground 3 meters from its base. When Leah walks 2.5 meters from the base of the pole toward the point where the cable is attached to the ground, her head just touches the cable. Leah is 1.5 meters tall. How many meters tall is the pole?
X = 3-2.5 = 0.5 m.
Y = 1.5 m.
Tan A = Y/X = 1.5/0.5 = 3.0
A = 71.57o
Tan 71.57 = h/3
Solve for h.
9 meters
To find the height of the pole, we can set up a right triangle using the given information.
Let's assume that the height of the pole is represented by 'h'.
Using the Pythagorean theorem, we have:
(h + 1.5)^2 = 2.5^2 + h^2
Expanding and simplifying,
h^2 + 3h + 2.25 = 6.25 + h^2
Simplifying further,
3h = 6.25 - 2.25
3h = 4
h = 4/3
Therefore, the pole is 4/3 meters tall.
To find the height of the pole, we can use similar triangles and the concept of proportions.
Let's label the height of the pole as "h" meters.
We are given that Leah walks 2.5 meters from the base of the pole towards the point where the cable is attached to the ground. At this point, her head just touches the cable. Leah's height is 1.5 meters.
From the given information, we can create two similar right triangles: the larger triangle that includes the height of the pole (h) and the smaller triangle formed by Leah's height (1.5 meters) and the distance she walked (2.5 meters) towards the cable attachment point.
By the property of similar triangles, we know that corresponding sides of similar triangles are proportional. In this case, we can set up the proportion:
(height of the pole)/(distance walked by Leah) = (height of Leah)/(distance between Leah and cable attachment point)
(h)/(2.5) = (1.5)/(3)
Now we can solve for h by cross-multiplying:
h * 3 = 1.5 * 2.5
h * 3 = 3.75
Dividing both sides of the equation by 3:
h = 3.75 / 3
h = 1.25
Therefore, the height of the pole is 1.25 meters.