A lookout spots a fire from a 32 meter tower.The angle of depression from the tower to the fire is 13 degrees. To the nearest meter, how far is the fire from the base of the tower? answer
Tan13 = 32/x
32 ft/ tan 13
138.60 = 139
139 = x
Well, well, well, it seems like we have a burning question here. Let me help you put out those doubts!
Since we have an angle of depression of 13 degrees, we can use some trigonometry to solve this riddle. The angle of depression forms a right triangle with the tower and the distance to the fire.
So, let's call the distance from the base of the tower to the fire 'x'. Now, the tangent of the angle of depression is equal to the opposite side (32 meters, the height of the tower) over the adjacent side (the distance to the fire 'x').
Therefore, we can set up the equation: tan(13 degrees) = 32 meters / x.
Now, let's do some calculations and solve this equation. Drumroll, please...
x = 32 meters / tan(13 degrees) ≈ 135 meters.
So, the fire is approximately 135 meters away from the base of the tower. Keep a safe distance, my friend, and remember, no clowning around with fires!
To find the distance from the base of the tower to the fire, we can use trigonometry. Let's assume that the distance from the base of the tower to the fire is "x" meters.
Using the angle of depression of 13 degrees, we can create a right triangle with the tower, the ground, and a line connecting the base of the tower to the fire.
The angle of depression is the angle between the line of sight from the top of the tower to the fire and the horizontal ground. Therefore, the angle between the line connecting the base of the tower to the fire and the vertical height of the tower is also 13 degrees.
We know that tangent of an angle is equal to the opposite side divided by the adjacent side in a right triangle. In this case, the opposite side is the height of the tower (32 meters) and the adjacent side is the distance from the base of the tower to the fire (x meters).
So we have: tan(13 degrees) = opposite (32 meters) / adjacent (x meters).
To find x, we rearrange the equation: x = opposite (32 meters) / tan(13 degrees).
Using a scientific calculator, calculate the tangent of 13 degrees:
tan(13 degrees) ≈ 0.224951
Now, substitute the values into the equation:
x = 32 meters / 0.224951
x ≈ 142.2414 meters
Rounding to the nearest meter, the fire is approximately 142 meters from the base of the tower.