A triangle has two sides of length 40 cm and an angle of 110°.a) Determine the length of the third side. Then find the perimeter of the triangle.47b) Determine the area of the triangle

Answer:a) c = 65.532 cmP = 145.532 cmb) A = 751.754 cm²Step-by-step explanation:This is an isosceles triangle.  The given angle is obtuse, so it must be the vertex angle.a) One way to find the length of the third side is law of cosine:c² = a² + b² − 2ab cos Cc² = 40² + 40² − 2(40)(40) cos 110°c = 65.532Another way is to cut the triangle in half and use sine.sin (110°/2) = (c/2) / 40c = 80 sin 55°c = 65.532The perimeter is the sum of the sides:P = 40 + 40 + 65.532P = 145.532b) You can find the area using the SAS equation:A = ½ ab sin CA = ½ (40)(40) sin 110°A = 800 sin 110°A = 751.754Another way is to split the triangle in half, find the height using cosine, then use half the base times height.cos (110°/2) = h / 40h = 40 cos 55°h = 22.943A = ½ chA = ½ (65.532) (22.943)A = 751.754