Question

A surveyor is standing opposite of two points (a and c) on the river. The two points are 900 ft. The surveyor is 653 ft from both a and c. What is the angle formed at the surveyed?

a) 37.5 degrees
b) 60 degrees
c) 90 degrees
d) 120 degrees

Answer 1

a) 37.5 degrees. To find the angle formed at the surveyor, we can use the law of cosines.

Step-by-step explanation:

To find the angle formed at the surveyor, we can use the law of cosines. Let's call the distance between the two points (a and c) on the river 'b'. The law of cosines states that c^2 = a^2 + b^2 - 2ab*cos(C), where 'c' is the distance between the surveyor and both points, 'a' is the distance between the two points, and 'C' is the angle formed at the surveyor. Plugging in the known values, we have 900^2 = 653^2 + 653^2 - 2*653*653*cos(C). Solving for cos(C), we get cos(C) = (900^2 - 2*653^2)/(2*653*653). Taking the inverse cosine of this value, we find that the angle formed at the surveyor is approximately 37.5 degrees (option a).