at 10:00 am on April 26, 2006, a building 300 feet high casts a shadow 50 feet long. What is the angle of elevation of the sun?
To find the angle of elevation of the sun, we can use the tangent function. 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 building, which is 300 feet, and the adjacent side is the length of the shadow, which is 50 feet.
Let's call the angle of elevation of the sun "θ". So, we can set up the equation:
tan(θ) = opposite/adjacent
tan(θ) = 300/50
Now, we can solve this equation to find the angle of elevation, θ.
Using a calculator or a table of tangents, we can find the inverse tangent of 300/50:
θ = arctan(300/50)
θ ≈ 80.5377 degrees
Therefore, the angle of elevation of the sun is approximately 80.54 degrees.
as always
(a) draw a diagram
(b) review your basic trig functions
Then it will be clear that
tanθ = 300/50