Question

1. looking down from a 21 - foot tower, a forest ranger spots a fire on the ground. the angle of depression from the tower to the fire is $12^{circ}$. a. draw a diagram to represent this situation. b. to the nearest foot, how far is the fire from the base of the tower? show all steps. bonus: a 16 - foot ladder is placed against the side of a building as shown in figure 1 below. the bottom of the ladder is 8 feet from the base of the building. in order to increase the reach of the ladder against the building, the ladder is moved 4 feet closer to the base of the building as shown in figure 2. to the nearest foot, how much farther up the building does the ladder now reach? show how you arrived at your answer.

Explanation:

Step1: Calculate the initial height

Use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c = 16\) (ladder length) and \(a = 8\) (initial base distance).

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Step2: Calculate the new height

Now \(a = 4\) (new base distance), \(c = 16\) (ladder length).

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Step3: Calculate the difference in height

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Answer:

The ladder now reaches approximately \(2\) feet farther up the building.