webassign net O Lesson 476s The stewart Precalloulus triangl

webassign net O Lesson 47:6s The stewart, Precalloulus triangle ealo find A o... twostraight roads dive O al1 points I Provious Answers SPrecalc7 6.5033 To find the distance across a river, a surveyor chooses points A and B, which are x 100 ft apart on one side of the river (see the figure). She then chooses reference point Con the opposite side of the river and finds that LBAC 82. and LABc.s2 Approximate the distance from c. (Round your answer to the nearest foot.) 82° 52 Need Help? RendE Home My Assgnments Extension Reques

Solution

In the ABC, we have BAC = 82⁰ and ABC = 52⁰. Since the sum of the internal angles of a triangle is 180⁰, therefore the ACB = 180⁰-82⁰-52⁰ =46⁰. Now, as per the sine formula, we have AC/sin52⁰ = x/sin46⁰ or, AC = x(sin52⁰/ sin46⁰) = 100(sin52⁰/ sin46⁰) = 100(0.788/0.0.719) = 109.60 ft. or, 110 ft approximately( on rounding off to the nearest foot.)