a tree cast a shadow 25 feet long. the angle of elevation from the far end of the shadow to the top of the tree is 64 degrees,find the heighth of the tree
(height)/25 = tan64 = 2.05
height = 51.3 (ft.)
I assume that you are familiar with trigonometric functions such as tangent, although you have indicated geometry as the subject.
To find the height of the tree, we can use trigonometry. Let's consider the given information:
The length of the shadow (adjacent side) = 25 feet
The angle of elevation (opposite side) = 64 degrees
We need to find the height of the tree (opposite side).
We can use the tangent function (tan) to relate the angle of elevation to the opposite and adjacent sides. The formula is:
tan(angle) = opposite / adjacent
Substituting in the given values, we have:
tan(64 degrees) = height of the tree (opposite) / 25 feet (adjacent)
Now, we can solve for the height of the tree by rearranging the formula:
height of the tree = tan(64 degrees) * 25 feet
Calculating this using a calculator, the height of the tree is approximately 56.87 feet.
Therefore, the height of the tree is approximately 56.87 feet.
To find the height of the tree, we can use trigonometry. Specifically, we can use the tangent function.
Let's call the height of the tree "h".
We know the length of the shadow is 25 feet, and the angle of elevation is 64 degrees.
Using the tangent function, we can set up the following equation:
tan(64 degrees) = h / 25
To solve for "h", we can multiply both sides of the equation by 25:
25 * tan(64 degrees) = h
Now we can calculate this value using a scientific calculator or an online calculator. Taking the tangent of 64 degrees gives us approximately 2.1445.
Therefore:
h ≈ 25 * 2.1445
h ≈ 53.61 feet
So, the height of the tree is approximately 53.61 feet.