Final answer:
To find the height of the billboard, we can use trigonometry and the given angles of elevation. For the first problem, we use the tangent function to calculate the height. For the second problem, we use the sine function to find the height of the telephone pole.
Step-by-step explanation:
Problem 1:
Let's use trigonometry to solve this problem. We have a right triangle formed by the building, the bottom of the billboard, and the top of the billboard. We are given the angle of elevation from the base of the building to the bottom of the billboard (25 degrees) and the angle of elevation from the base of the building to the top of the billboard (41 degrees). We can use the tangent function to find the height of the billboard.
We know that:
tan(angle) = opposite/adjacent
In this case, the adjacent side is the distance from the base of the building to the bottom of the billboard (124 ft). The opposite side is the height of the billboard (h).
So, we have:
tan(25 degrees) = h/124 ft
By solving for h, we find that the height of the billboard is approximately 53.19 ft.
Problem 2:
This problem involves a right triangle formed by the wire, the telephone pole, and the ground. We are given the length of the wire (100 ft), the distance from the top of the pole to where the wire is attached (5 ft), and the angle the wire makes with the ground (30 degrees). We can use the sine function to find the height of the pole.
We know that:
sin(angle) = opposite/hypotenuse
In this case, the hypotenuse is the length of the wire (100 ft). The opposite side is the height of the pole (h + 5 ft, where h is the height of the pole above the point of attachment).
So, we have:
sin(30 degrees) = (h + 5 ft)/100 ft
By solving for h, we find that the height of the telephone pole is approximately 51.96 ft.