Zola can see the top of 180m cell phone at an angle of elevation of 32 degrees, and Naeem can see it an angle of elevation of 50 degrees. How far apart are Zola and Naeem if they are on a straight line with the tower? There are two possibilities.
X1 m.= Naeem's distance from base of tower.
X2 = distance between Zola and Naeem.
X1+X2 = Zola's distance from base of tower.
Tan 50 = h/X1 = 180/X1.
X1 = 180/Tan50 = 151 m.
Tan32 = 180/(X1+X2) = 180/(151+X2).
(151+X2) = 180/Tan32 = 288.
X2 = 137 m.
To find the distance between Zola and Naeem, we can use trigonometry.
Let's assume the distance between Zola and the cell tower is x meters. Then, the distance between Naeem and the cell tower would also be x meters, as they are on the same straight line.
Zola can see the top of the cell phone at an angle of elevation of 32 degrees. Using trigonometry, we can set up the equation:
tan(32 degrees) = height of the tower / distance between Zola and the tower
Since the height of the tower is 180 meters, we can rearrange the equation to solve for the distance between Zola and the tower:
distance between Zola and the tower = height of the tower / tan(32 degrees)
distance between Zola and the tower = 180 / tan(32 degrees)
Similarly, Naeem can see the top of the cell phone at an angle of elevation of 50 degrees. Using the same logic, we can set up the equation:
distance between Naeem and the tower = height of the tower / tan(50 degrees)
distance between Naeem and the tower = 180 / tan(50 degrees)
Therefore, the two possibilities for the distance between Zola and Naeem are:
1) distance between Zola and Naeem = (180 / tan(32 degrees)) + (180 / tan(50 degrees))
2) distance between Zola and Naeem = (180 / tan(32 degrees)) - (180 / tan(50 degrees))
By evaluating these two equations, you will find the respective distances between Zola and Naeem.