To The Nearest Degree,find The Angle Of Elevation Of The Sun When A 9 Meters Vertical Casts A Shadow 3 Meters Long.
tan(Θ) = 9 m / 3 m
Good
tan(Θ)=9m/3m
tan(Θ)=3.0m
Θ=tan^-1(3.0m)
Θ~72°
To find the angle of elevation of the sun, you can use the tangent function. The tangent of an angle is equal to the length of the opposite side divided by the length of the adjacent side. In this case, the opposite side is the height of the vertical (9 meters) and the adjacent side is the length of the shadow (3 meters).
Therefore, the tangent of the angle of elevation is given by:
tan(angle of elevation) = opposite/adjacent
tan(angle of elevation) = 9/3
tan(angle of elevation) = 3
To find the angle of elevation, you need to take the inverse tangent (also known as arctan or tan^(-1)) of both sides:
angle of elevation = arctan(3)
Calculating this value, you will get:
angle of elevation ≈ 71.57 degrees
So, to the nearest degree, the angle of elevation of the sun when a 9 meters vertical casts a shadow 3 meters long is approximately 72 degrees.