At a certain time, a vertical pole 3 meters tall casts a 4 meter shadow. What is the angle of elevation of the sun? Round your answer to the nearest meter
Since when is angles in meters?
tanTheta=3/4
theta= arctan .75
how do u turn 1095millionths into scientific notation
To find the angle of elevation of the sun, we need to use the concept of similar triangles, where the height of the pole corresponds to the length of the shadow.
In this case, we have a vertical pole that is 3 meters tall and casts a 4-meter shadow.
Let's assume that the angle of elevation of the sun is θ.
Using trigonometry, we know that the tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the height of the pole (3 meters) and the adjacent side is the length of the shadow (4 meters).
So, we can write the equation:
tan(θ) = opposite/adjacent
tan(θ) = 3/4
To find the angle θ, we can take the inverse tangent (or arctan) of both sides of the equation:
θ = arctan(3/4)
Using a calculator, we can find the arctan(3/4) to be approximately 36.87 degrees.
Rounding this to the nearest degree, we get the angle of elevation of the sun to be 37 degrees.