How to solve a vertical pole 8 feet tall cast a shadow 5 feet long on level ground.find the angle which the rays of the sun makes with the horizontal.
A ladder 16feet long makes an angle of 53O with the ground as it leans against a store. To the nearest hundredth , how far up the store does the ladder reach.
A vertical pole 8 feet tall cast a shadow 5 feet long on level ground. Find the angle which the rays of the sun make with the horizontal
Well, you know what they say about shadows, right? They're like mischievous accomplices, always trying to confuse us! But fear not, dear friend, for I shall shed some light on this matter!
To find the angle the sun's rays make with the horizontal, we can use some math-fu. As we know, the shadow is cast by the pole, which means it forms a right triangle with the pole and the ground.
So, the tangent of the angle, let's call it theta (θ), is equal to the length of the opposite side (the height of the pole) divided by the length of the adjacent side (the length of the shadow). In this case, that would be 8 feet divided by 5 feet.
Now, it's time to grab your trusty calculator or put those math skills to work. Calculate the arctangent (inverse tangent) of 8/5, and Voila! You'll have your angle with the horizontal in all its glory. Let's see if we can shed some light on that!
θ = arctan(8/5)
Go ahead, crunch that equation, and may the mathematical gods be with you, my friend!
To find the angle the rays of the sun make with the horizontal, we can use trigonometry. In this case, we can use the tangent function.
The tangent of an angle is equal to the opposite side divided by the adjacent side. In this scenario, the opposite side is the height of the pole (8 feet) and the adjacent side is the length of the shadow (5 feet).
Therefore, the tangent of the angle θ (theta) is given by:
tan(θ) = opposite side / adjacent side
tan(θ) = 8 feet / 5 feet
Now, we can use a scientific calculator to find the inverse tangent (also known as arctan or tan⁻¹) of this value to determine the angle:
θ = tan⁻¹(8 / 5)
Using a scientific calculator, the angle θ is approximately 58.28 degrees.
So, the angle which the rays of the sun make with the horizontal is approximately 58.28 degrees.
After you sketch your triangle, you should see that
tanØ = 8/5 <----- opposite/adjacent
Ø= appr 58° , using my calculator