Algebra question

Question

You are measuring the width of the river. You place a stake on one side of the river, directly across from a rock and walk 100 meters to the right of the stake and measure a 79° angle between the stake and the rock. Draw a sketch and find the width of the river to the nearest tenth?

Answer 1

tan(79)= W/100

W=100tan79= 100(5.145) =514.5 meters

or

cot(90-79) = W/100 = 100 cot 11 = 514.5 meters

cot11 = tan 79

it's a right triangle with angles, 90, 79 and 11 degrees

Answer 2

This forms a right triangle with the near adjacent side being 100 meters and the opposite side being the width.

We can ignore the hypotenuse. The tangent of 79 Deg is equal to the width divided by 100 meters.

tan(79) = opposite/adjacent = w/100 ---> w = 100tan(79) = 100(5.1445540) =514.5 to the nearest tenth.