The distance between two buildings is labeled in red below. You can see the closest edge of each building with an angle of view of 65° . Your distance to one edge is 22m and to the other is 17 m. To find the distance between the two buildings (red), will you use Law of Sines or Law of Cosines? What is the distance?
To find the distance between the two buildings (labeled in red), we will use the Law of Cosines, as we have two sides (your distance to each building) and the included angle (angle of view).
The Law of Cosines states that:
c^2 = a^2 + b^2 - 2ab cos(C)
Where c is the unknown distance (red line), a is 22m, b is 17m, and C is the angle of view (65°).
Plugging in the values:
c^2 = (22)^2 + (17)^2 - 2(22)(17) cos(65°)
c^2 = 484 + 289 - 748 cos(65°)
c^2 = 773 - 748(0.42262)
c^2 = 773 - 316.06
c^2 = 456.94
Taking the square root of both sides:
c = √456.94
c ≈ 21.37m
Therefore, the distance between the two buildings is approximately 21.37 meters.