a man 5 ft tall casts a shadow of 6 ft. The angle of elevation f the sun is?
TanA = Y/X = 5/6
To find the angle of elevation of the sun, we can use basic trigonometry.
We know that the height of the man (opposite side) is 5 ft and the length of his shadow (adjacent side) is 6 ft.
Using the tangent function, we can find the angle of elevation (θ) as follows:
tan(θ) = opposite/adjacent
tan(θ) = 5/6
To find the angle, take the inverse tangent (arctan) of both sides:
θ = arctan(5/6)
Using a calculator, the angle of elevation (θ) will approximately be 39.81 degrees.
Therefore, the angle of elevation of the sun is approximately 39.81 degrees.
To find the angle of elevation of the sun, you can use the trigonometric relationship between the height of the object and the length of its shadow.
First, let's define the height of the object as h and the length of its shadow as s.
In this case, the man's height is 5 ft and his shadow is 6 ft. We need to find the angle of elevation of the sun, which is the angle between the horizontal ground level and the line from the top of the man's head to the sun.
To find the angle, we can use the tangent function (tan):
tan(angle) = h / s
Plugging in the given values:
tan(angle) = 5 / 6
Now, to find the angle, we need to take the inverse tangent (arctan) of both sides:
angle = arctan(5 / 6)
Using a calculator or a trigonometric table, you can find that the arctan(5 / 6) is approximately 40.56 degrees.
Therefore, the angle of elevation of the sun is approximately 40.56 degrees.