In △abc, m∠a = α, m∠b = β, m∠c = γ. ab = c, ac = b, bc = a. find the areas of the triangles if the following parts are given.
a=5, b=7, γ=31º

9514 1404 393

  9.01 square units

Step-by-step explanation:

The area of the triangle is given by the formula ...

  Area = 1/2ab·sin(C)

  Area = (1/2)(5)(7)sin(31°) ≈ 9.01 . . . . square units

so the possibilities of the measurement of the side of the triangle are either it is longest side or not the longest side

when it is the longest side

s < 25 + 35s < 60

if it is not the longest side

35 < 25 + s10 < sso 10 < s < 60so the perimeter70 < p < 130

step-by-step explanation:

assume that you have 3 different side lengths.   apply the pythagorean theorem here:   square each of the two shortest sides; call them a and b, so that their squares are a² and b².   also square the longest side, calling the result c².

now, if a² + b² = c² is true, the triangle is a right triangle; otherwise it is not a right triangle.