Greg and ann are standing on a river bank 180 meters apart at points A and B respectively (see figure) they want to know the distance from ann to a house across the river at point C greg measures angle A (angle BAC) to be 49 °and ann measures angle B ( angle ABC) to be 58 ° what is the distance from ann to the house round your answer to the nearest tenth of a meter

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

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step-by-step explanation: