In a triangle ABC, if angle A=40 degree and angle B=65 degree, determine the shortest and largest sides of the - Maths - Triangles

Question

In a triangle ABC, if angle A=40 degree and angle B=65 degree,
determine the shortest and largest sides of the triangle

Shipra D. · Accepted Answer

We should know length of atleast one side in order to find the
other sides Since, it is not mentioned in the question so I am
assuming it to be 22 75 cm In a triangle
∠A+∠B+∠C=180°⇒40°+65°+∠C=180°⇒105°+∠C=180°⇒∠C=75°Since,
∠A is the smallest so the length (a) of the side opposite to
∠A will be the shortest Also, since ∠C is the largest
so the length (c) of the side opposite to ∠C will be the
largest Consider the Sine formula,asinA=bsinB=csinCThe length (b)
of side opposite to ∠B=22 75 cmTherefore, we
haveasin40°=22 75sin65°⇒a=22 75×0 640 91=16
cmAlso, 22 75sin65°=csin75°⇒c=22 75×0 960 91=24
cmThus, length of the largest side is 24 cm and length of the
shortest side is 16 cm

In a triangle ABC, if angle A=40 degree and angle B=65 degree, determine the shortest and largest sides of the triangle.