Points a and b are on opposite sides of a lake. a point c is 91.791 meters from a. the measure of ∠bac ∠ b a c is 76.833°, and the measure of ∠acb ∠ a c b is determined to be 31.683°. find the distance between points a and b.

We're given two angles and an included side and we want to solve for a side opposite one of the given angles. Using the typical triangle notation we have

b=AC=91.791 meters

A=76.833 degrees

C=31.683 degrees

and our task is to find c=AB.

To apply the Law of Sines we need B, which we get since the triangle angles add to 180 degrees:

B = 180 - A - C = 180 - 76.833 - 31.683 = 71.484 degrees

Now the Law of Sines says

50.842 meters

< coa = 150 ( given)

as ba and bc are tangents

so oc and oa is perpendicular to cb and ab respectively because in circle normal passes through centre

so in quadrilateral oabc

< coa + < oab + < ocb + < abc = 360

150 +90+90 + < abc = 360

330 + < abc = 360

< abc = 360 -330 = 30

so < abc = 30

⭐dhruv⭐

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step-by-step explanation: