At a certain time of the day, a 4-meter-tall vertical pole casts a shadow of 3 meters. What is the angle of elevation, to the nearest degree, of the Sun?
tan ( theta ) = 4 / 3
theta = inverse tangent ( 4 / 3 )
theta = 53 ° 7 ´ 48 "
theta = 53 ° to the nearest degree
a woman stands 3ft from a track her shadow is 6ft long how tall is woman
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To find the angle of elevation of the Sun, we can use the tangent function. The tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side in a right triangle.
In this case, the 4-meter-tall pole is the vertical side of the right triangle, and its shadow of 3 meters is the horizontal side. The angle we are looking for is the angle of elevation of the Sun, which is the angle between the ground (horizontal) and the line from the top of the pole to the Sun (hypotenuse).
Let's denote the angle of elevation as θ. According to the tangent function:
tan(θ) = opposite/adjacent
In this case, the opposite side is the height of the pole (4 meters), and the adjacent side is the length of its shadow (3 meters). Therefore:
tan(θ) = 4/3
To find θ, we need to take the inverse tangent (or arctan) of both sides:
θ = arctan(4/3)
Using a calculator, we can find that θ is approximately 53.13 degrees. Rounding to the nearest degree, the angle of elevation of the Sun is 53 degrees.