. A vertical mast is 83.5m high. Calculate the angle of of elevation of its top
from a point 12cm away on level ground.
tan^-1 (height/distance away)
Surely 12 cm is a typo but if true use 0.12 meters
sorry Damon can you please explain more
tangent of the angle of elevation = height of mast / distance to mast
and I simply do not believe you are only 12 CENTIMETERS from the mast.
To calculate the angle of elevation of the top of the vertical mast from a point on level ground, we can use trigonometry.
First, let's draw a diagram to visualize the situation. We have a vertical mast of height 83.5m, and a point on level ground that is 12cm away from the mast.
|
| /|
| / |
| / | 83.5m
|/___|
12cm
In this diagram, the line from the top of the mast to the point on the ground creates a right triangle. The height of the mast (opposite side) is given as 83.5m, and the distance from the mast to the point on the ground (adjacent side) is 12cm. We are trying to find the angle of elevation (theta).
To find the angle of elevation, we can use the trigonometric function called tangent (tan). The tangent of an angle is equal to the ratio of the opposite side to the adjacent side.
Tan(theta) = opposite/adjacent
In our case, tan(theta) = 83.5m / 12cm.
However, we need to make sure our units are consistent. Since the height of the mast is given in meters, we should convert the distance on the ground from centimeters to meters. There are 100 centimeters in a meter, so 12cm = 12/100 = 0.12m.
Thus, tan(theta) = 83.5m / 0.12m.
Now we can calculate the angle of elevation theta by taking the inverse tangent (arctan) of both sides of the equation:
theta = arctan(83.5m / 0.12m)
Using a calculator or trigonometric table, we find that:
theta ≈ 87.995 degrees.
Therefore, the angle of elevation of the top of the mast from the point on the ground is approximately 87.995 degrees.