The shadow of a tower on level ground increases by 16 m when the altitude of the sun changes from 60° to 45°. As shown in the figure below: As we need to find the height of the tower:

The shadow of a tower standing on a level ground is found to be 40 m longer when Suns altitude is 30 than when it was 60. Find the height of the tower.

To solve this problem, we can use the concept of similar triangles. The tower and the post cast shadows at the same time, which means the angle of elevation of the sun is the same for both, creating two similar triangles. Let's denote the height of the tower as \( h \) and the length of its shadow as 114 ft. We are given that a 9.0-ft post casts an 8.0-ft long shadow. We can set up a proportion using the corresponding sides of the similar triangles: \[ \frac{\text{Height of post}}{\text{Length of post's shadow}} = \frac{\text{Height of tower}}{\text{Length of tower's shadow}} \] Substituting the given values: \[ \frac{9.0}{8.0} = \frac{h}{114} \] Now we can solve for \( h \): \[ h = \frac{9.0}{8.0} \times 114\] \[ h = 1.125 \times 114\] \[ h = 128.25 \text{ ft} \] Rounding to the nearest unit, the height of the tower is approximately 128 feet.

A man wants to measure the height of a nearby tower. He places a 6ft pole in the shadow of the tower so that the shadow of the pole is exactly covered by the shadow of the tower. The total length of the tower's shadow is 198ft, and the pole casts a shadow that is 4.25ft long. How tall is the tower? Round your answer to the nearest foot.

A tree casts a shadow 24ft long from its base with an angle of elevation of the sun of 40° How tall is the tree?*15.43 ft12 ft12.34 ft20.14 ft

Find the angle of elevation of the sun if a building 78 meters high, cast a shadow of 45 meters.*29.98°60.18°