Answer:
The building the ladder reaches is 18 ft rounded up to the nearest foot
Explanation:
The wall of a building is horizontal and it is perpendicular to the ground (makes an angle 90° with the ground.
The foot of the ladder forms an angle of 65° with the ground.
With this illustration, a right angled triangle is constructed.
From trigonometry, we have SohCahToa.
This means that the sine function is given by
Sine Φ = opposite / hypothenuse
Φ = the angle between the hypotenuse and the adjacent sides
The opposite side, opp is the side of the right angled triangle directly opposite to the given angle, the hypotenuse is the side opposite the angle of intersection between the wall and the floor.
We are given, Φ = 65°, opp = the height of the building, h
hyp = the height of the ladder = 20ft
Therefore, sin 65 = h/20ft
We cross multiply to get,
h = 20ftsin65
h = 18ft to the nearest foot