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 $\mathrm { N } 31 ^ { \circ } \mathrm { W }$ .The developer leaves point A and travels 74 yards perpendicular to $\overline{A B}$ to point C.The bearing from C to point B is $\mathrm { N } ~59 ^ { \circ } \mathrm { W }$ .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 $\mathrm { N } 31 ^ { \circ } \mathrm { W }$ .The developer leaves point A and travels 74 yards perpendicular to $\overline{A B}$ to point C.The bearing from C to point B is $\mathrm { N } ~59 ^ { \circ } \mathrm { W }$ .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

Using trigonometry, we can find the length of the line segment AC:

sin(90-11ea99db_b4bb_b778_94ac_3fddcefa3848_TB4590_11) = AC/74
sin(11ea99db_b4bb_b778_94ac_3fddcefa3848_TB4590_11) = AC/74
AC ≈ 70.13 yards

Now, we can use the angle between AB and CB (which is 90 degrees) to find the length of AB:

sin(90-11ea99db_b4bb_b779_94ac_41851d287bf1_TB4590_11) = AB/AC
sin(11ea99db_b4bb_b779_94ac_41851d287bf1_TB4590_11) = AB/AC
AB ≈ 138.6 yards

Rounding to the nearest yard, we get AB ≈ 139 yards. So the answer is C.

A Land Developer Wants to Find the Distance Across a Small