Answer:
17.2 meters
Explanation:
We can use the tangent function to solve this problem. Let's denote the height of the tree as h. Then we have the following:
tan(51°) = h / distance from the tree to the end of the shadow
We can find the distance from the tree to the end of the shadow by using the length of the shadow and the angle of elevation of the sun. Since the shadow is 21 meters long, and the angle of elevation of the sun is 51°, we can use the following trigonometric relationship:
tan(51°) = h / distance from the tree to the end of the shadow
tan(51°) = h / x (where x is the distance from the tree to the end of the shadow)
To find x, we can use the following trigonometric relationship:
tan(39°) = h / x (where 39° is the complementary angle to 51°)
We can solve for x by rearranging this equation as follows:
x = h / tan(39°)
Substituting this expression for x into the first equation, we have:
tan(51°) = h / (h / tan(39°))
Simplifying this equation, we get:
h = (21 m) * tan(51°) / tan(39°)
Using a calculator, we find h to be the following:
h = 17.2 meters
Therefore, the height of the tree is approximately 17.2 meters.