Tabitha is looking up at a bird's nest in a tree. The angle of elevation is 74.5^(∘), and she is standing 12 feet away from the tree's base. Her eyes are 5 feet above the ground. We will find the height of the bird's nest. Let's x be the height of the bird's nest from Tabitha's eyes.
Let's write an equation using a trigonometric function that includes a ratio of the height of the bird's nest from Tabitha's eyes and the horizontal distance between her eyes and the bird's nest. To do so we will use tangent. Remember that the tangent of θ is the ratio between the lengths of the opposite side and the adjacent side.
tan θ = Opposite/Adjacent ⇒ tan 74.5^(∘) = x/12
Now we will solve the equation for x.
The height of the bird's nest from Tabitha's eyes is about 43 feet, but we want to find the height of the bird's nest from the ground. To do so we will add the height of Tabitha's eyes from the ground: 5 feet.
43+ 5=48 feet
The height of the bird's nest from the ground is about 48 feet.
