Answer :
Answer: 114.37 ft
Step-by-step explanation:
If we model this situation as a right triangle, where the hypotenuse is the length of the ladder ([tex]110 ft[/tex]), the opposite leg is the height the ladder will reach [tex]h[/tex], and the adjacent leg is the distance between the base of the ladder and the building ([tex]28 ft[/tex]); we have two options:
1) Using trigonometric functions, since we are given the angle [tex]\theta=75\°[/tex]
2) Using the Pithagorean Theorem
Any of the options will give a similiar result. So, let's choose the Pithagorean Theorem:
[tex](hypotenuse)^{2}=(opposite-leg)^{2}+(adjacent-leg)^{2}[/tex]
[tex](110 ft)^{2}=(h)^{2}+(28 ft)^{2}[/tex]
Isolating [tex]h[/tex]:
[tex]h=\sqrt{(110 ft)^{2}-(28 ft)^{2}}[/tex]
[tex]h=106.37 ft[/tex]
Adding to this height the extra height of [tex]8 ft[/tex] (since the base of the ladder is at this distance above the ground, perhaps held by a firefighter truck):
[tex]h=106.37 ft+8 ft=114.37 ft[/tex] This is the height the ladder will reach