Final answer:
To calculate the height the ladder reaches on the building, we use the sine function with the given 77-degree angle and the 18-foot length of the ladder, obtaining approximately 17.54 feet.
Step-by-step explanation:
The student asks how high a ladder of 18 feet reaches on a building when it is leaning at an angle of 77 degrees to the ground. To answer the question, we can use trigonometry. Specifically, the sine function relates the opposite side of a right-angled triangle (in this case, the height reached on the building) to the hypotenuse (the ladder) and the angle between the hypotenuse and the adjacent side (the angle at the base, which is 77 degrees).
The formula for sine is given by:
sin(Θ) = opposite/hypotenuse
Here, Θ is the given angle of 77 degrees, the opposite side is the unknown height we want to find (let's call it h), and the hypotenuse is the length of the ladder, which is 18 feet. Hence, we can write:
sin(77°) = h/18 ft
The next step is to calculate h using the following rearranged equation:
h = 18 ft × sin(77°)
Using a calculator, we can find the value of h
h ≈ 18 ft × 0.97437 ≈ 17.54 ft
Therefore, the ladder reaches approximately 17.54 feet high on the building, when rounded to the hundredth place.