SOLUTION: 13. Atiba wants to measure the width of the Hudson River. Standing under a tree T on the river bank, Atiba sights a rock at the nearest point R on the opposite bank. Then Atiba wal

Algebra ->  Trigonometry-basics -> SOLUTION: 13. Atiba wants to measure the width of the Hudson River. Standing under a tree T on the river bank, Atiba sights a rock at the nearest point R on the opposite bank. Then Atiba wal      Log On


   

Question 148137: 13. Atiba wants to measure the width of the Hudson River. Standing under a tree T on the river bank, Atiba sights a rock at the nearest point R on the opposite bank. Then Atiba walks to a point P on the river bank that is 50 meters from T, and makes RTP a right angle. Atiba then measures RPT and obtains 76.8 degrees. How wide is the river?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First let's draw a picture of the problem:

Photobucket - Video and Image Hosting


From the picture, we can see that the opposite side is "x" and the adjacent side is 50. So let's use the tangent function to find the unknown length

Remember, the tangent function is tan%28a%29=opposite%2Fadjacent where "a" is the angle


tan%28a%29=opposite%2Fadjacent Start with the given equation.


tan%2876.8%29=x%2F50 Plug in a=76.8 and the given lengths of the legs of the triangles.


50tan%2876.8%29=x Multiply both sides by 50.


50%284.264%29=x Take the tangent of 76.8 to get 4.264 (note: make sure that you are in "degree" mode)


213.2=x Multiply


So the answer is approximately x=213.2 which means that the width of the river is about 213.2 meters