At a certain time, a verical pole 10 feet tall casts a 14-foot shadow. What is the angle of elevation of the sun to the nearest degree?
To find the angle of elevation of the sun, you need to use the ratio of the height of the pole to the length of its shadow. This can be done using trigonometry, specifically with tangent.
The tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. In this case, the height of the pole is opposite to the angle of elevation, and the length of the shadow is adjacent to the angle.
Let's label the angle of elevation as θ. Using tangent, we have:
tan(θ) = (height of the pole) / (length of the shadow)
Substituting the given values, we have:
tan(θ) = 10 / 14
To find the angle θ, we can take the inverse tangent (arctan) of both sides:
θ = arctan(tan(10 / 14))
Using a calculator, we find:
θ ≈ 36.87 degrees
Therefore, the angle of elevation of the sun, to the nearest degree, is 37 degrees.
To find the angle of elevation of the sun, we can use the trigonometric concept of tangent. Tangent is defined as the ratio of the opposite side (the height of the pole) to the adjacent side (the length of the shadow).
In this case, the height of the pole is 10 feet and the length of the shadow is 14 feet. Therefore, the tangent of the angle of elevation is:
tangent(angle) = opposite/adjacent
tangent(angle) = 10/14
To find the angle, we can take the inverse tangent (also known as arctangent) of both sides:
angle = arctan(tangent(angle))
angle = arctan(10/14)
Calculating this value using a scientific calculator or an online calculator, we find that:
angle ≈ 36.87 degrees
Therefore, the angle of elevation of the sun, to the nearest degree, is approximately 37 degrees.
tanA = Y/x = 10/14 = 0.71429.
A = 35.5 Deg.