Final answer:
To find the length of the shadow cast by a 22-meter pole, we use proportions based on similar triangles formed by a 12-meter pole and its 26.4-meter shadow. Calculating using the ratio, we find the shadow to be 58.4 meters long.
Step-by-step explanation:
The question asks us to find the length of the shadow cast by another pole given the height of one pole and the length of its shadow. This is a problem that can be solved using similar triangles in geometry. When a pole casts a shadow due to sunlight, the angles of elevation are the same for all objects as the sun's rays are considered parallel. Therefore, the poles and their shadows form similar triangles, meaning their sides are in proportion.
The height of the first pole is given as 12 meters with a shadow of 26.4 meters. The height of the second pole is 22 meters. We can set up a proportion since the triangles are similar:
Height of first pole / Length of first pole's shadow = Height of second pole / Length of second pole's shadow
This gives us:
12 / 26.4 = 22 / x
Where x is the length of the second pole's shadow. Solving for x, we get:
x = (22 * 26.4) / 12
x = 58.4 meters
Therefore, the length of the shadow of a 22-meter pole is 58.4 meters.