Final answer:
Using the angle of elevation and trigonometry, the squirrel is determined to be approximately 19.2 feet off the ground when rounded to the nearest tenth.
Step-by-step explanation:
To determine how many feet off the ground the squirrel is, we can use trigonometry. Specifically, we'll use the tangent function, which relates the angle of elevation to the height and distance from the observer. Given the angle of elevation to the squirrel is 21°, we can set up our equation using the formula tan(θ) = opposite/adjacent. Here, the opposite side is the height of the squirrel above the ground, which we want to find (h), and the adjacent side is the distance from the fire tower to the tree, which is given as 50 feet.
Applying the formula, we have:
tan(21°) = h/50
Solving for h:
h = 50 × tan(21°)
When you calculate this, you'll get the height of the squirrel above the ground. Note that the angle of depression to the base of the tree is not needed for this particular calculation.
Let's do the math:
h = 50 × tan(21°) ≈ 50 × 0.383864
Therefore:
h ≈ 19.1932
To answer the question, rounding to the nearest tenth, the squirrel is 19.2 feet off the ground.