Height of an Obelisk Two people decide to find the height of an obelisk. They position themselves 25 feet apart in line with, and on the same side of, the obelisk. If they find that the angles of elevation from the ground where they are standing to the top of the obelisk are 65 degrees and 44 degrees, how tall is the obelisk?

To find the height of the obelisk, we can use trigonometry.

Let's call the distance from one person to the obelisk as "x" and the height of the obelisk as "h."

From the first person's perspective, the angle of elevation is 65 degrees. This means that the opposite side is "h" and the adjacent side is "x + 25."

Using the tangent function, we can write the following equation:

tan(65) = h / (x + 25)

From the second person's perspective, the angle of elevation is 44 degrees. This means that the opposite side is "h" and the adjacent side is "x."

Again, using the tangent function, we can write the following equation:

tan(44) = h / x

Now, we have two equations with two unknowns (h and x). We can solve this system of equations to find the values of h and x.

First, let's isolate h in both equations:

Equation 1: h = (x + 25) * tan(65)

Equation 2: h = x * tan(44)

Setting these two expressions for h equal to each other, we have:

(x + 25) * tan(65) = x * tan(44)

Now, we can solve this equation for x:

x * tan(44) = (x + 25) * tan(65)

Simplifying the equation:

x * (tan(44) - tan(65)) = 25 * tan(65)

Now, divide both sides by (tan(44) - tan(65)) to solve for x:

x = (25 * tan(65)) / (tan(44) - tan(65))

Once you calculate the value of x, you can substitute it back into either equation to find the height of the obelisk, h.

h = x * tan(44)

So, to determine the height of the obelisk, you need to calculate the value of x using the formula above and substitute it into the equation for h.

draw a diagram. If the height is h and the closer person is x feet from the base of the obelisk,

h/x = tan65°
h/(x+25) = tan44°

h/(h cot65°+25) = tan44°
h = 43.9 ft

seems like a small obelisk.