A tree casts a shadow 203 feet long. Find the number of feet in the height
of the tree knowing that the angle of elevation of the sun is 16 degrees. Give
your answer to the nearest integer.
a. 57
b. 56
c. 61
d. 58
e. 55
height --- x
solve for x
tan16 = x/203
58!! I'm workin on it too! LOL! See you in class!
To find the height of the tree, we can use the concept of trigonometry. Let's understand the problem first.
The shadow of the tree forms a right triangle with the tree itself and the sun. The length of the shadow (203 feet) represents the base of the triangle, and the height of the tree represents the opposite side. The angle of elevation of the sun (16 degrees) is the angle between the base and the hypotenuse of the triangle.
We need to find the height of the tree, which is the length of the opposite side.
To find the length of the opposite side, we can use the trigonometric function "tangent." The tangent of an angle is defined as the ratio of the opposite side to the adjacent side in a right triangle.
In our case, the opposite side is the height of the tree, and the adjacent side is the length of the shadow. So we can set up the following equation:
tan(16 degrees) = height of the tree / length of the shadow
Now, we need to solve this equation for the height of the tree.
First, we can find the tangent of 16 degrees using a scientific calculator or an online tool. The tangent of 16 degrees is approximately 0.2867.
Substituting this value and the length of the shadow (203 feet) into the equation, we get:
0.2867 = height of the tree / 203
To find the height of the tree, we can cross-multiply the equation:
height of the tree = 0.2867 * 203
Calculating this, we get:
height of the tree ≈ 58.199 feet
However, we are asked to give our answer to the nearest integer. Rounding 58.199 to the nearest integer, we get:
height of the tree ≈ 58 feet
So the answer is option d. 58.