Juicu, the firefighter, was standing at top of an observation tower when he saw a fire. The angle of depression from the observation tower to the fire was 60°. A kid is trapped half way between the base of the tower and the fire. The height of the tower is 90 feet. What is the shortest distance Juicu has to travel to save the kid? - no flying possible

Answer: 160 ft to reach the kid. Plus some miles before he and Juicu are safe.

Step-by-step explanation:

Trig functions are remembered by

SOD CAD TOA,

sin = opposite / distance, cos = adjacent / distance, and tan = opposite / adjacent.

This time we need TOA.

We assume the area is flat and level. We know the angle (60°) and the opposite side of a right triangle with adjacent side running parallel to the ground to the fire, and opposite side running 90 feet straight down to the fire.

The angle of depression is 60° (?!). Then the fire is closer than the tower is high, and we better evacuate. The minimum distance traveled to rescue the kid has to include getting away from the tower ... Assume we want to know how far to travel to reach the kid.

Since this is a 30-60-90 triangle, the sides are 1, 1/2, and √3/2 = 1.732/2 = 0.866. (1732 was the year of George Washington's birth). That means sin (60°) = 0.866 ... nevermind. It's easier to use trig functions and they work when the angles aren't 30°, 45°, or 90°, and everyone carries trig functions in their phone.

Angle is 60°, opposite side is 90 feet, opposite side divided by adjacent side is tan (60°), adjacent side is opposite side divided by tan (60°) = 90ft/tan (60°) = 51.9615242ft, the kid is half way between base of tower and fire = 25.9807621ft from the base of the tower, and we have to travel 90+25.9807621 = 116.0 feet to reach the kid (hopefully before the fire travels 26 feet.)