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, we can use the tangent function.
The height of the pole is 10 feet, and the length of the shadow is 14 feet. Let's label the angle of elevation as θ.
The tangent of θ is the opposite side (height of the pole) divided by the adjacent side (length of the shadow):
tan(θ) = opposite/adjacent
= 10/14
= 5/7
Now, we need to find the angle whose tangent is 5/7. To do this, we can use the inverse tangent function (also known as arctan or atan).
So, θ = arctan(5/7).
Using a calculator or lookup table, we can find the tangent inverse of 5/7.
arctan(5/7) ≈ 36.87 degrees.
Therefore, the angle of elevation of the sun to the nearest degree is approximately 37 degrees.
To find the angle of elevation of the sun, we can use trigonometry. The height of the pole and the length of its shadow form a right triangle.
Let's call the angle of elevation of the sun θ. The opposite side of the triangle is the height of the pole (10 feet), and the adjacent side is the length of the shadow (14 feet).
The tangent of an angle in a right triangle is defined as the ratio of the length of the opposite side to the length of the adjacent side. So we can use the formula:
tan(θ) = opposite/adjacent
In this case, tan(θ) = 10/14.
Now, we can find the angle θ by taking the inverse tangent (arctan) of both sides of the equation:
θ = arctan(10/14)
Using a calculator, we can evaluate this expression:
θ ≈ 36.87 degrees
Therefore, the angle of elevation of the sun to the nearest degree is approximately 37 degrees.