A lookout spots a fire from a 36 meter tower the angel of depression from the tower to the fire is 21 degrees . To the nearest meter how far is the fire from the base of the tower
tan21 = 36/X. Solve for X
To solve this problem, we can visualize a right triangle formed by the tower, the distance from the base of the tower to the fire, and the line of sight from the lookout to the fire.
The angle of depression is the angle formed between the line of sight from the lookout to the fire and the horizontal line parallel to the ground. In this case, the angle of depression is 21 degrees.
In a right triangle, the tangent function relates the angle to the sides of the triangle. The formula is:
tan(angle) = opposite/adjacent
In this case, the opposite side is the height of the tower (36 meters) and the adjacent side is the distance from the base of the tower to the fire (which we want to find).
So, we can write the equation as:
tan(21 degrees) = 36m/adjacent
To find the adjacent side, we rearrange the equation:
adjacent = 36m / tan(21 degrees)
Now, we can calculate the adjacent side using a calculator:
adjacent = 36m / tan(21 degrees)
adjacent ≈ 97.04m
Therefore, to the nearest meter, the fire is approximately 97 meters from the base of the tower.