A wall 9ft high cast a shadow of 15ft. Find the angle of the sun rays with the ground.
Routine use of trig in a right-angled triangle, assuming the wall is vertical and the ground is horizontal
tan θ = 9/15
θ = tan^-1 (9/15) = appr 31°
Ah, the great mystery of the shadow and the sun. Well, I must admit, I'm not much of a shadow scholar, but I can certainly give it a shot!
Let's see here. If the wall is 9ft high and it casts a shadow of 15ft, it means the shadow is longer than the wall itself. Quite the overachiever, that shadow!
To find the angle of the sun's rays with the ground, we can use a little trigonometry. The tangent of an angle tells us the ratio of the opposite side (in this case, the shadow) to the adjacent side (in this case, the height of the wall).
So, the tangent of the angle = shadow/height = 15/9.
Now, I'm no math whiz, but if we plug this into a tangent calculator, it should give us the answer. Drumroll, please... the angle of the sun's rays with the ground is approximately 58.2 degrees!
And there you have it! The angle of the sun's rays with the ground is 58.2 degrees, or as I like to call it, the "shadow slinger angle." Enjoy basking in the mathematical glory!
To find the angle of the sun rays with the ground, we can use the tangent function.
Tangent (θ) = Opposite / Adjacent
In this case, the opposite side is the height of the wall (9ft) and the adjacent side is the length of the shadow (15ft).
Tangent (θ) = 9ft / 15ft
Now we can calculate the angle.
θ = arctan (9/15)
Using a scientific calculator, we can find the inverse tangent (arctan) of 9/15.
θ ≈ 30.96 degrees
Therefore, the angle of the sun rays with the ground is approximately 30.96 degrees.
To find the angle of the sun rays with the ground, we need to use trigonometry. The height of the wall represents the opposite side, and the length of the shadow represents the adjacent side of a right triangle.
Let's define the angle between the ground and the sun rays as θ. We can use the tangent function to calculate θ since it relates the opposite and adjacent sides of a right triangle.
The tangent of an angle is given by the formula:
tan(θ) = opposite/adjacent
In this case, the opposite side is the height of the wall (9ft), and the adjacent side is the length of the shadow (15ft).
tan(θ) = 9/15
To solve for θ, we need to take the inverse tangent (also known as arctangent or tan^(-1)) of both sides of the equation:
θ = tan^(-1)(9/15)
Using a calculator, you can find the inverse tangent of 9/15, which is approximately 30.96 degrees.
Therefore, the angle of the sun rays with the ground is approximately 30.96 degrees.