Answer:
a) c = 65.532 cm
P = 145.532 cm
b) A = 751.754 cm²
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