To find the angle measures of the shore where the lighthouses and the ship are located, we need to use the fact that the sum of the angles of a triangle is 180 degrees1. We can write an equation for each triangle and solve for x, then substitute x into the expressions for the angles. Here are the steps:
For triangle ABS, we have:
7
x
+
30
+
13
x
+
5
+
3
x
=
180
7x+30+13x+5+3x=180
Simplifying and solving for x, we get:
23
x
+
35
=
180
23x+35=180
23
x
=
145
23x=145
x
=
6.3
x=6.3
For the angle at A, we have:
7
x
+
30
=
7
(
6.3
)
+
30
7x+30=7(6.3)+30
7
x
+
30
=
74.1
7x+30=74.1
For the angle at B, we have:
13
x
+
5
=
13
(
6.3
)
+
5
13x+5=13(6.3)+5
13
x
+
5
=
86.9
13x+5=86.9
For the angle at S, we have:
3
x
=
3
(
6.3
)
3x=3(6.3)
3
x
=
18.9
3x=18.9
Therefore, the angle measure of the shore where lighthouse A is located is 74.1 degrees, the angle measure of the shore where lighthouse B is located is 86.9 degrees, and the angle measure of the shore where the ship is located is 18.9 degrees