Avacant lot is in the shape of an isosceles triangle. it is between two streets that intersect at an 85.9degree angle. each of the sides of the lot that face these streets is 150 ft. long. find the perimeter of the lot to the nearest foot.

1. An isosceles triangle has two equal sides and you have the length of these sides (a=105 feet), but you need the other one: "b". So, if you a draw a segment that bisects the angle of 85.9°,you will obtain two equal right triangles, as you can see in the figure attached. Now, you have to find the value of "x" and the side "b" will be 2x:

 Sin(α)=Opposite/Hypotenuse

 α=89.5°/2=42.95°
 Opposite=x
 Hypotenuse=105

 Sin(42.95°)=x/105
 x=(105)(Sin(42.95°))
 x=71.54 feet

 2. Then the other side of the isosceles triangle (b), is:

 b=2x
 b=2x71.54 feet
 b=143.08 feet

 3. The perimeter of the isosceles triangle, is:

 P=2a+b
 P=2(105 feet)+143.08 feet
 P=210 feet+143.08 feet
 P=353 feet