Find the perimeter and area of an isosceles triangle whose vertex angle is 35 degrees and whose two equal sides each measure 15 cm

Answer 1

isosceles triangle has vertex angle = 35 degrees and 2 sides = 15 cm

other 2 angles are each (180-35)/2 = 145/2 = 72.5 degrees

base = 3rd side = b cm

divide the triangle in half down the middle

creating 2 right triangles each with base = b/2

cos72.5 = (b/2)/15 = b/30 = about 3/10

solve for b=9.02 = about 9

perimeter = 15+15+9.02 = 39.02 about 39 cm

area = 1/2 x 15 x 15 sin35 = about 64.527 cm^2

or

area = 1/2 x hb = h/2(9.02) = 4.51h

h/15 = sin72.5 = about .954

h = 15(.954)

area = 4.51(15)(.954)=about 64.52

more accurate area= 64.53 cm^2