Question

A monument in the shape of a right triangle sits on a rectangular pedestal that is 5 meters high by 11 meters long. The longest side of the triangular monument measures 61 meters. How high off the ground is the top of the monument?

Answer 1

Based on the information given, there are 2 possibilities:
1) the hypotenuse is the base of the triangles, sitting on the rectangular pedestal
2) the right angle touches the pedestal, with the base equalling the pedestal length

In 1) it is pretty straightforward, because the right angle is the apex (top). The base is 61m, because the longest side in a right is always the hypotenuse.
So now we need the height (h), which will split the triangle into two 45-45-90 triangles with base and h = 30.5 (1/2 the initial base)
This will make the height off the ground = 30.5+5 = 35.5 m

2) with right angle touching the pedestal, we can only assume that the base equals the pedestal length, 11. Then we need the missing side (h), which we can derive from Pythagorean Theorem:
${h}^{2} = {61}^{2} - {11}^{2} \\ \sqrt{({h}^{2})} = \sqrt{({61}^{2} - {11}^{2})} \\ h = \sqrt{({61}^{2} - {11}^{2})} = \sqrt{(3721- 121)} \\ h= \sqrt{3600} = 60$
So in this triangle the height off ground would be 60+5 = 65 m