General Triangle Story Problems Please Help Tonight

[boston1234]

I really don't understand these problems at all. Please Help thanks.
1.The navigator of a ship took two sightings on a lighthouse. The first was 36 degrees from the craft's heading. AFter traveling 8 km, The angle was 150 degrees from the same heading. What were the two distances from the boat to the lighthouse?
2. The side of a hill has a slope of 60.2 with the horizontal. A sighting of the top of the hill taken 100 m from the base shows 27.6. What is the distance up the side from the base to the top of the hill?

 

[Deleted member 4993]

I really don't understand these problems at all. Please Help thanks.
1.The navigator of a ship took two sightings on a lighthouse. The first was 36 degrees from the craft's heading. AFter traveling 8 km, The angle was 150 degrees from the same heading. What were the two distances from the boat to the lighthouse?
2. The side of a hill has a slope of 60.2 with the horizontal. A sighting of the top of the hill taken 100 m from the base shows 27.6. What is the distance up the side from the base to the top of the hill?

First draw a sketch of the situation - for both the cases.

1) Then use definition of "tan" of an angle.

2) Using the technique of (1) first find the height of the mountain. Then use definition of "Sine" to find the distance up the slope.

 

[soroban]

Hello, boston1234!

1.The navigator of a ship took two sightings on a lighthouse.
The first was 36 degrees from the craft's heading.
After traveling 8 km, the angle was 150 degrees from the same heading.
What were the two distances from the boat to the lighthouse?

                  L
                  *
               *      *
            *             *
         *  36d         30d  * 150d
    A * - - - - - - - - - - - - * B - - - - * E
                   8

\(\displaystyle \text{The ship sights lighthouse }(L)\text{ at }A:\;\;\angle LAB = 36^o\)

\(\displaystyle \text{It travels 8 km to }B:\;AB \:=\:8\)

. . \(\displaystyle \text{And: } \:\angle LBE = 150^o \quad\Rightarrow\quad \angle LBA = 30^o\)


\(\displaystyle \text{In }\Delta ALB\text{, we have two angles and the included side.}\)

. . \(\displaystyle \text{Use the Law of Sines to find sides }LA\text{ and }LB.\)