Final answer:
Using trigonometry with a 60° angle and a 26-foot long ladder, we find the height of the building h by calculating h = 26 × cos(60°), which gives us 13 feet.
Step-by-step explanation:
To find the height of the building, we can use trigonometry since we have a right triangle formed by the ladder, the ground, and the wall of the building. The ladder makes a 60° angle with the ground and its length is 26 feet. The equation that relates these is given by the cosine of the angle, which is the adjacent side (the height of the building, h) over the hypotenuse (the ladder).
The equation is:
cos(60°) = h / 26
To solve for the height h, multiply both sides of the equation by the length of the ladder:
h = 26 × cos(60°)
Calculate h by applying the value of cos(60°), which is 0.5:
h = 26 × 0.5
h = 13 feet
Therefore, the height of the building is 13 feet.