Final answer:
To calculate the distance of the man from the base of the building across the square measured along his line of sight, we can use trigonometry. Label the height of the man as x and the distance as y. Form two right triangles using the angles of depression and solve for x and y.
Step-by-step explanation:
To calculate the distance of the man from the base of the building across the square measured along his line of sight, we can use trigonometry. Let's label the height of the man as x and the distance as y. From the angle of depression of the base of the building, we can form a right triangle with the height of the man as the opposite side, the distance as the adjacent side, and the angle of depression as the angle. This gives us the equation tan(40°) = x/y. Similarly, we can form another right triangle for the angle of depression of the top of the building, giving us the equation tan(25°) = (x+48.5)/y.
From these two equations, we can solve for x and y using the properties of trigonometric functions. First, solve the equation tan(40°) = x/y for x, giving us x = y * tan(40°). Then substitute this value of x into the second equation, tan(25°) = (y * tan(40°) + 48.5)/y, and solve for y. Once you have the value of y, you can substitute it back into the first equation to find x.