Answer :
Final answer:
The distance from point A is 3.09
Explanation:
Radio direction finders are devices used to determine the direction to a transmitter. In this scenario, two direction finders are located at points A and B, which are 4.44 miles apart on an east-west line. The transmitter has specific bearings from points A and B, which are 39.3 degrees and 313.9 degrees, respectively.
A from T = 39.3° +180° = 219.3°
B from T = 313.9° -180° = 133.9°
Then the angle at T between receivers is ...
219.3° -133.9° = 85.4°
The angle between A and T as measured at B will be ...
313.9° -270° = 43.9°
These angles and length AB can be used with the Law of Sines to find AT:
AT/sin(B) = AB/sin(T)
AT = AB(sin(B)/sin(T)) = (4.44 mi)·sin(43.9°)/sin(85.4°)
AT = 3.09
Answer:
3.09 miles
Step-by-step explanation:
Given one distance and two angles, we will need to use the Law of Sines. For this, we need to know the internal angles of the triangle formed by the various bearing lines.
The angle between the bearings of A and B from the transmitter will be the difference of the reverse of the given bearings.
A from T = 39.3° +180° = 219.3°
B from T = 313.9° -180° = 133.9°
Then the angle at T between receivers is ...
219.3° -133.9° = 85.4°
The angle between A and T as measured at B will be ...
313.9° -270° = 43.9°
These angles and length AB can be used with the Law of Sines to find AT:
AT/sin(B) = AB/sin(T)
AT = AB(sin(B)/sin(T)) = (4.44 mi)·sin(43.9°)/sin(85.4°)
AT ≈ 3.09 mi
The distance of the transmitter from A is about 3.09 miles.