Ralph the monkey is looking down at a 31° angle from the top of a tree. There are bananas on the ground 12.4 ft from the base of the tree. If Ralph flies down from the tree at a diagonal path, shown in the diagram by x, what distance would he travel? Round to the nearest hundredth.
Not knowing the path without a diagram, I don't have a clue.
However, the slant distance is
12.4/sin31
To find the distance Ralph would travel, we need to determine the length of the diagonal path shown by x in the diagram.
First, let's break down the problem. We have a right triangle formed by Ralph's line of sight, the distance from the base of the tree to the bananas, and the diagonal path Ralph would take. The line of sight and the diagonal path form the legs of the triangle, and the distance from the base of the tree to the bananas is the hypotenuse.
Using trigonometric ratios, specifically the tangent function, we can find the length of the diagonal path:
tan(θ) = opposite/adjacent
In this case, θ is the angle Ralph is looking down (31°). The opposite side is the distance from the base of the tree to the bananas (12.4 ft), and we need to find the length of the diagonal path (x). Rearranging this equation, we get:
x = tan(31°) * 12.4 ft
Now, we can plug in the values and calculate the length of the diagonal path:
x = tan(31°) * 12.4 ft
x ≈ 0.601 \* 12.4 ft
x ≈ 7.4604 ft
Rounded to the nearest hundredth, Ralph would travel approximately 7.46 ft along the diagonal path.