A bridge is to be built across a small lake from a gazebo to a dock. The bearing from the gazebo to the dock is S 41° W. From a tree x = 100 meters from the gazebo, the bearings to the gazebo and the dock are S 74° E and S 28° E, respectively (see figure in the link below). Find the distance from the gazebo to the dock. (Round your answer to the nearest whole number.)

Question

A bridge is to be built across a small lake from a gazebo to a dock. The bearing from the gazebo to the dock is S 41° W. From a tree x = 100 meters from the gazebo, the bearings to the gazebo and the dock are S 74° E and S 28° E, respectively (see figure in the link below). Find the distance from the gazebo to the dock. (Round your answer to the nearest whole number.) 
www.webassign.net/larprecalcaga5/7-1-028-alt.gif

anonymous · Accepted Answer

my answer is (100sin46)/sin69 = 77.1m is my answer correct?

Damon · Answer

distance TD = 100 m GTD = 74-28 = 46 deg TDG = 28 + 41 = 69 deg TGD = 180 - 74-41 = 65 deg now is 46 + 69 + 65 = 180? Yes, remarkable we have a triangle so sin 46/GD = sin 65/100

Damon · Answer

I have angle at G = 65 You have 69 which I had at the dock

Damon · Answer

Whoops sorry I did the tree to the dock

anonymous · Answer

sin 46/GD = sin 65/100 =(100sin46)/sin65=79.37 is this correct?

anonymous · Answer

so (100sin46)/sin69 = 77.1 is correct?

Damon · Answer

yes I did the wrong leg

anonymous · Answer

hey damon thanks,
can you help me on this question:
A plane flies 505 kilometers with a bearing of 316° (clockwise from north) from Naples to Elgin. The plane then flies 770 kilometers from Elgin to Canton (see figure in the link below). Canton is due west of Naples. Find the bearing of the flight from Elgin to Canton. (Round to the nearest whole number.)
www.webassign.net/larpcalclim2/6-1-048-alt.gif