A land developer wants to find the distance across a small lake in the middle of his proposed development.The bearing from A to B is .The developer leaves point A and travels 74 yards perpendicular to to point C.The bearing from C to point B is .Determine the distance, AB, across the small lake.Round distance to nearest yard.
A)169 yards
B)114 yards
C)139 yards
D)154 yards
E)121 yards

Question

A land developer wants to find the distance across a small lake in the middle of his proposed development.The bearing from A to B is  .The developer leaves point A and travels 74 yards perpendicular to  to point C.The bearing from C to point B is  .Determine the distance, AB, across the small lake.Round distance to nearest yard. 
A)169 yards 
B)114 yards 
C)139 yards 
D)154 yards 
E)121 yards

Quizplus · Accepted Answer

- Draw a diagram and label the points A, B, C, and D as shown here: https://imgur.com/a/OGJdAqh
- Let x be the distance from C to D, the point on line AB directly below C.
- Using trigonometry, we can find that tan(11°14'38") = x/74, so x = 74tan(11°14'38").
- Let y be the distance from D to B. Using trigonometry again on triangle CDB, we can find that tan(11°14'29") = y/x, so y = xtan(11°14'29").
- Finally, AB = y+74. Plugging in the values we found for x and y, we get AB = 138.6 yards. Rounded to the nearest yard, the answer is 139 yards (choice C).

A Land Developer Wants to Find the Distance Across a Small