A rocket reaches a height of 300 √3 m. A crowd observing the launch stands 300 m away. What is the maximum angle θ, in which the crowd observes the launch.
30 degrees
45 degrees
60 degrees
75 degrees
tan x = 300 sqrt 3 /300 = sqrt 3
around 60 degrees :)
( 30 60 90 triangle)
To determine the maximum angle θ at which the crowd observes the launch, we can use the concept of trigonometry. The tangent function relates the height and distance to the angle. The formula is:
tan(θ) = (height)/(distance)
Given that the height is 300√3 m and the distance is 300 m, we can substitute these values into the formula:
tan(θ) = (300√3)/(300)
Simplifying, we cancel out the common factor of 300:
tan(θ) = √3
Now, we need to find the angle θ that has a tangent of √3. To do this, we can use the inverse tangent function, also known as arctan or tan^(-1). This function will give us the angle when given a tangent.
θ = arctan(√3)
Using a calculator, we can find the value of arctan(√3) to be approximately 60 degrees.
Therefore, the maximum angle θ at which the crowd observes the launch is 60 degrees.
To find the maximum angle θ at which the crowd observes the launch, we can use trigonometry. We have a right triangle where the height of the rocket is the opposite side, the distance to the crowd is the adjacent side, and the angle θ is the unknown angle.
We can use the tangent function to find the angle θ. The tangent of an angle is equal to the ratio of the opposite side to the adjacent side:
tan(θ) = (opposite) / (adjacent)
In this case, the opposite side is the height of the rocket (300√3 m) and the adjacent side is the distance to the crowd (300 m).
Plugging in the values:
tan(θ) = (300√3) / 300
Simplifying:
tan(θ) = √3
To find the value of θ, we can use the inverse tangent function (also known as arctangent or tan^-1). Taking the inverse tangent of both sides:
θ = tan^-1(√3)
Using a calculator, we find:
θ ≈ 60 degrees
Therefore, the maximum angle θ at which the crowd observes the launch is approximately 60 degrees.