A student is trying to calculate the height of a tree. She measures the shadow to be 15 yards long at 3:00 p.m. At this time the angle of elevation of the sun is appoximately 68 degrees. How tall is the tree?
tan 68 = height/15
height is then in yards, if you want feet multiply by three.
A bird sits on top of a lamppost. The angle of depression from the bird to the feet of an observer standing away from the lamppost is 35 degrees. The distance from the bird to the observer is 25 meters. How tall is the lamppost?
To calculate the height of the tree, we can use trigonometry. In this case, we can use the tangent function because we have the length of the shadow and the angle of elevation of the sun.
We know that the tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the height of the tree and the adjacent side is the length of the shadow.
Let's represent the height of the tree as 'h' (in yards). The length of the shadow is given as 15 yards. The angle of elevation is given as 68 degrees.
Using the tangent function, we can set up the following equation:
tan(68 degrees) = h / 15 yards
To solve for 'h', we can rearrange the equation:
h = tan(68 degrees) * 15 yards
Now, we can calculate the value of 'h':
h = tan(68 degrees) * 15 yards
Using a scientific calculator or trigonometric table, we find that the approximate value of tan(68 degrees) is 2.9174.
Substituting this value into the equation, we get:
h = 2.9174 * 15 yards
Calculating the product, we find that:
h ≈ 43.76 yards
Therefore, the height of the tree is approximately 43.76 yards.