if =65 tan "o"(theta sign), what is the approximate change in h when (theta sign) changes from 60 degree to 60°03’.
h = 65tan(x)
dh = 65 sec^2(x) dx
Now plug in your values for x and dx (in radians!)
To find the approximate change in h when θ changes from 60 degrees to 60°03', we need to use the given equation: h = 65 tanθ.
First, let's calculate the value of h for θ = 60 degrees:
h₁ = 65 tan(60°)
= 65 √3
≈ 112.23
Next, let's calculate the value of h for θ = 60°03'. To do this, we need to convert the seconds into degrees:
1 minute = 1/60 degree
1 second = 1/3600 degree
θ₂ = 60° + 0°03'
= 60° + (3/60)°
= 60.05°
h₂ = 65 tan(60.05°)
At this point, we can use either a scientific calculator or an online trigonometric calculator to find the value of h₂. Let's use an online calculator:
h₂ ≈ 112.285
Now, we can calculate the change in h by subtracting h₁ from h₂:
Δh = h₂ - h₁
≈ 112.285 - 112.23
≈ 0.055
Therefore, the approximate change in h when θ changes from 60 degrees to 60°03' is approximately 0.055.