at a certain time , a post 6 ft tall casts a 3 ft shadow.what is the angle of elevation of th sun
arctan (post height)/(shadow length)
= arctan(6/3) = arctan2
= 63.44 degrees
To determine the angle of elevation of the sun, we can use the ratio of the height of the object to the length of its shadow. In this case, we have a post that is 6 ft tall casting a shadow that is 3 ft long.
The tangent function can be used to find the angle. The formula for tangent is:
tan(angle) = opposite/adjacent
In this case, the height of the post is the opposite side, and the length of the shadow is the adjacent side. Therefore, we can solve for the angle of elevation as follows:
tan(angle) = 6/3
Dividing 6 by 3 gives us:
tan(angle) = 2
Now, we need to find the angle whose tangent is 2. To do this, we can use the inverse tangent function, also known as arctan or atan.
angle = arctan(2)
Using a scientific calculator or an online calculator that supports trigonometric functions, we can find that:
angle ≈ 63.4 degrees
Therefore, the angle of elevation of the sun is approximately 63.4 degrees.