A 12-meter high post casts a 19-meter shadow. Find the angle of elevation to the sun.

-what is/are given?
-formula used
-solution

help me pls. my head is spinning

review your basic trig functions. Draw a diagram. Note that

tanθ = 12/19

now you can find θ.

.632?

What will be the given ?

Shift tan (12÷19)

To find the angle of elevation to the sun, we can use the concept of similar triangles.

Given:
Height of the post (opposite side): 12 meters
Length of the shadow (adjacent side): 19 meters

Now, let's define the angle of elevation (θ) as the angle between the horizontal ground and the line from the top of the post to the sun. We need to find this angle.

Formula Used:
In a right triangle, the tangent of an angle θ is defined as the ratio of the length of the opposite side to the length of the adjacent side. Mathematically, it can be represented as:
tan(θ) = Opposite/Adjacent

Solution:
In this case, the length of the opposite side is 12 meters (height of the post) and the length of the adjacent side is 19 meters (length of the shadow). So, the equation becomes:
tan(θ) = 12/19

To find θ, we need to take the inverse tangent (also known as arctan) of both sides. This will give us the angle in degrees:
θ = tan^(-1)(12/19)

Using a calculator, we can solve for the angle of elevation θ. It is approximately 32.7 degrees.

Therefore, the angle of elevation to the sun is approximately 32.7 degrees.