Lines, angles, and triangles SAT question

Choice B is correct. Each tree and its shadow can be modeled using a right triangle, where the height of the tree and the length of its shadow are the legs of the triangle. At a given point in time, the right triangles formed by two nearby trees and their respective shadows will be similar. Therefore, if the height of the other tree is $x$, in feet, the value of $x$ can be calculated by solving the proportional relationship $\frac{10\text{feet tall}}{5\text{feet long}}=\frac{x\text{feet tall}}{2\text{feet long}}$. This equation is equivalent to$\frac{10}{5}=\frac{x}{2}$, or $2=\frac{x}{2}$. Multiplying each side of the equation $2=\frac{x}{2}$ by $2$ yields $4=x$. Therefore, the other tree is $4\text{feet}$ tall.

Choice A is incorrect and may result from calculating the difference between the lengths of the shadows, rather than the height of the other tree.

Choice C is incorrect and may result from calculating the difference between the height of the $10$-foot-tall tree and the length of the shadow of the other tree, rather than calculating the height of the other tree.

Choice D is incorrect and may result from a conceptual or calculation error.