You measure the shadow cast by a certain tall building and find that it is 105 feet long. then you measure the shadow by a three foot post and find that is 4 inches long. determine the buildings height

4 inches = 1/3 of a foot.

The post is 3 foot, the shadow is 1/3 foot

Find the scale factor:

3 / 1/3 = 3*3/1 = 9.

The post is 9 times longer than the shadow.

This means the building is 9 times bigger than it' shadow:

105 x 9 = 945

The building is 905 feet tall.

No, the triangular numbers are not a direct variation. There is not a constant of variation between a number and its position in the sequence. The ratios of the numbers to their positions are not equal. Also, the points (1, 1), (2, 3), (3, 6), and so on, do not lie on a line.

Hope this helps!!! :)