Three towns, A, B and C, are positioned relative to each other as follows: • Town B is 68 km from A on a bearing of 225°. • Town C is on a bearing of 135° from A. • Town C is on a bearing of 090" from B. a Drawing a sketch if necessary, deduce the distance from A to C. b Calculate the distance from B to C.
Answers
Answered by
0
Answer:
By the Law of Sines, we know that:
sin
a
x
=
sin
110
34
=
sin
c
25
We can immediately solve for
c
.
sin
110
34
=
sin
c
25
25
sin
110
34
=
sin
c
c
=
sin
−
1
(
25
sin
110
34
)
The sum of angles in a triangle is
180
, so we can solve for a:
180
=
a
+
110
+
sin
−
1
(
25
sin
110
34
)
a
=
70
−
sin
−
1
(
25
sin
110
34
)
We now just need to solve the following equation for
x
:
sin
(
70
−
sin
−
1
(
25
sin
110
34
)
)
x
=
sin
110
34
34
sin
(
70
−
sin
−
1
(
25
sin
110
34
)
)
sin
110
=
x
None of the angles or values used are "standard" values on the unit circle, so this is the final answer.
Similar questions