A vertical pole 3m tall casts a shadow 1.8m long what is the angle?
tan theta = 3/1.8
I assume "the angle" is the angle from the tip of the shadow to the top of the pole.
To find the angle, we can use the properties of similar triangles. We know that the vertical pole and its shadow form two sides of a right triangle.
We can set up the following proportion:
(height of the pole) / (length of the shadow) = (hypotenuse of the right triangle) / (length of the opposite side)
Let's denote the angle we're trying to find as θ.
Now, let's substitute the known values into the proportion:
3 m / 1.8 m = hypotenuse / (1.8 * sinθ)
To isolate sinθ, we rearrange the equation:
sinθ = (3 / 1.8) / 1.8
Next, we calculate this value:
sinθ = 1.6667 / 1.8
Finally, we use the inverse sine function to find the angle θ:
θ = arcsin(1.6667 / 1.8)
Using a calculator, we find that arcsin(1.6667 / 1.8) ≈ 57.8 degrees.
Therefore, the angle θ between the pole and the ground is approximately 57.8 degrees.