At a certain time of the day a post, 4m tall, casts a shadow of 1.8m. What is the angle of elevation of the sun at that time?
tan theta = H / L
tan theta = 4 / 1.8 = 2.222222
theta = 65 ° 46 ´ 20 "
To find the angle of elevation of the sun, we can use the tangent ratio. The tangent of an angle is equal to the opposite side divided by the adjacent side.
In this case, the opposite side is the height of the post, which is 4m, and the adjacent side is the length of the shadow, which is 1.8m.
So the tangent of the angle of elevation (θ) can be calculated as:
tan(θ) = 4 / 1.8
Now, we can use the inverse tangent function (tan^(-1)) to find the angle:
θ = tan^(-1) (4 / 1.8)
Using a calculator, we can find that θ is approximately 65.15 degrees.
Therefore, the angle of elevation of the sun at that time is approximately 65.15 degrees.
To find the angle of elevation of the sun, we can use the trigonometric function tangent (tan). The tangent of an angle is the ratio of the opposite side (in this case, the height of the post) to the adjacent side (in this case, the length of the shadow).
Let's assign variables:
Height of the post (opposite side) = h = 4 m
Length of the shadow (adjacent side) = s = 1.8 m
Now we can calculate the angle:
1. Find the tangent of the angle:
tan(θ) = h / s
2. Substitute the values into the equation:
tan(θ) = 4 / 1.8
3. Use inverse tangent (arctan) to find the angle:
θ = arctan(4 / 1.8)
Using a scientific calculator or an online calculator, we can find the inverse tangent of 4 / 1.8, which is approximately 65.98 degrees.
Therefore, the angle of elevation of the sun at that time is approximately 65.98 degrees.