Atriangle 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.
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b) determine the area of the triangle

a) c = 65.532 cm

P = 145.532 cm

b) A = 751.754 cm²

Step-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 C

c² = 40² + 40² − 2(40)(40) cos 110°

c = 65.532

Another way is to cut the triangle in half and use sine.

sin (110°/2) = (c/2) / 40

c = 80 sin 55°

c = 65.532

The perimeter is the sum of the sides:

P = 40 + 40 + 65.532

P = 145.532

b) You can find the area using the SAS equation:

A = ½ ab sin C

A = ½ (40)(40) sin 110°

A = 800 sin 110°

A = 751.754

Another way is to split the triangle in half, find the height using cosine, then use half the base times height.

cos (110°/2) = h / 40

h = 40 cos 55°

h = 22.943

A = ½ ch

A = ½ (65.532) (22.943)

A = 751.754

40 x 50 = 2000

step-by-step explanation: