Try this word problem below.... Is my answer checking with yours?

Question

Sally is a surveyor in the badlands in South Dakota. At point A on the south side of a deep canyon, she sights across to a fire tower on the north side of the canyon at point B. Then she moves a measured 500 feet along the south rim of the canyon to a point C on a line perpendicular to her original sight line AB. Setting up her transit again, she finds that her line of sight, CB, to the tower is 81 degrees. Correct to the nearest whole foot, how far is point C from the tower?



I got
4783

Answer 1

According to your question, you have a right triangle ABC where angle BAC is 90 degrees and angle ACB is 81 degrees.
The length of side AC is 500 feet and you want to find side BC which is also the hypotenuse of the triangle. You will need to use cosine to solve.

cos 81 = 500/BC
BCcos 81 = 500
BC = 500/cos 81
BC = 3196 feet

Answer 2

tan = opposite / adjacent
thus

tan 81 = AB*500
500*tan 81 = AB
AB= 3156.75

using Pythagoras to find CB

CB^2 = sqrt (500^2 + 3156^2)

i got an answer of 3196 feet...