# The distance Shore Ita to Lake Edge is 28 km.Point Ilisum is north`/_L=59 degrees `,`/_S=36` what is distance to point Ilisum,area`DeltaPLS`   ` `Please explain

embizze | High School Teacher | (Level 2) Educator Emeritus

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Let P represent Point Ilisium, L the Lake Edge, and S the Shore Ita.

Draw triangle PLS. We are given `m/_L=59^@,m/_S=36^@,LS=28`

Using the Law of Sines we have the following extended proportion:

`(PL)/sinS=(PS)/sinL=(LS)/sinP` . Substituting the known values we get:

`(PL)/sin36^@=(PS)/sin59^@=28/sinP` . The measure of angle P is 180-(59+36)=85.

Then `PS=(28sin59^@)/sin85^@~~24.09`

Also `PL=(28sin36^@)/sin85^@~~16.52`

The area of the triangle is given by `"Area"=1/2 a b sinC` where C is the angle included between sides a and b.

So the area of triangle PLS is `"Area"=1/2(16.52)(28)sin59^@~~198.26`

So the distance from P to L is approxiamtely 16.52km, the distance from P to S is approximately 24.09km, and the area of the triangle is approximately 198.26 square km.