A meteorologist measures the angle of depression of a weather balloon as 53". A radio signal from the balloon indicates that it is 1680 feet from his receiver. How high is the weather balloon from the ground?
We can solve the problem with the help of trigonometry. Let's denote the height of the weather balloon from the ground as "h" and the distance between the meteorologist and the balloon as "d".
Since we know the angle of depression, we also know that the angle between the ground and the line of sight to the balloon is also 53 degrees (because the sum of angles in a triangle is 180 degrees).
Now we can use the tangent function to find the height of the balloon:
tan(53 degrees) = h / 1680 feet
Solving for h, we get:
h = 1680 feet * tan(53 degrees)
h ≈ 2019.78 feet
Therefore, the weather balloon is approximately 2019.78 feet high from the ground.
To find the height of the weather balloon from the ground, we can use trigonometry specifically the tangent function. The angle of depression, in this case, is the angle formed between a line of sight from the observer to the weather balloon and the horizontal line.
Let's denote the angle of depression as θ and the height of the weather balloon from the ground as h. The tangent function can be defined as the ratio of the opposite side (h) to the adjacent side (1680 feet) of the right triangle formed by the angle of depression.
So, we have the equation: tan(θ) = h/1680. We can rearrange this equation to solve for h.
h = tan(θ) * 1680
Now, let's substitute the given angle of depression into the equation. Given that the angle of depression is 53 degrees, we need to convert it into radians, as most mathematical trigonometric functions use radians as input.
θ = 53 degrees = 53 * (π/180) radians = 0.925 radians (approx)
Substituting the value of θ into the equation, we get:
h = tan(0.925) * 1680
Using a scientific calculator or performing the tangent calculation, we find:
h ≈ 38.122 feet
Therefore, the height of the weather balloon from the ground is approximately 38.122 feet.
To find the height of the weather balloon from the ground, we can use trigonometry, specifically the tangent function.
Let's denote the height of the weather balloon as h and the distance from the meteorologist's receiver to the weather balloon as d.
Given:
Angle of depression = 53 degrees
Distance from receiver to balloon (base) = 1680 feet
We can use the tangent function to find the height of the weather balloon:
tan(angle of depression) = height / distance from receiver to balloon
tan(53 degrees) = h / 1680 feet
To find the value of tan(53 degrees), we can use a calculator or reference table.
Using a calculator, we find:
tan(53 degrees) ≈ 1.327
Now we can rearrange the equation to isolate h:
h = tan(53 degrees) * 1680 feet
Plugging in the values, we can calculate the height of the weather balloon:
h ≈ 1.327 * 1680 feet
h ≈ 2227.76 feet
Therefore, the height of the weather balloon from the ground is approximately 2227.76 feet.