the angle of elevation of the sun is 78 degrees. How long is the shadow of a 30m tree?
30 m / x = tan(78º)
To determine the length of the shadow of the tree, we can use the concept of trigonometry. Specifically, we will use the tangent function.
The tangent of an angle is defined as the opposite side divided by the adjacent side of a right triangle. In this case, the opposite side is the height of the tree, and the adjacent side is the length of the shadow.
Let's denote the length of the shadow as 'x'. The height of the tree is given as 30m, and the angle of elevation of the sun is 78 degrees.
Using the tangent function, we can set up the following equation:
tan(78 degrees) = opposite / adjacent
tan(78 degrees) = 30 / x
Now, we need to solve for 'x'. The tangent of 78 degrees can be found using a scientific calculator or by looking it up in a table.
tan(78 degrees) ≈ 6.14487
Now, we can rewrite the equation as:
6.14487 = 30 / x
To find the value of 'x', we will rearrange the equation by multiplying both sides by 'x' and then dividing both sides by 6.14487:
x = 30 / 6.14487
Evaluating this, we find:
x ≈ 4.88
Therefore, the length of the shadow of the 30m tree is approximately 4.88 meters.