Centre of the hypotenuse

The interior angles of the triangle ABC, alpha, beta, and gamma are in a ratio of 1:2:3. The longest side of the AB triangle is 30 cm long. Calculate the perimeter of the triangle CBS if S is the center of the side AB.

Correct answer:

x =  45 cm

Step-by-step explanation:

α:β:γ=1:2:3  d=180/(1+2+3)=30   α=1 d=1 30=30  β=2 d=2 30=60  γ=3 d=3 30=90   AB=30 cm sin α = ABCB sin β = ABAC  CB=AB sinα=AB sin30° =30 sin30° =30 0.5=15 cm AC=AB sinβ=AB sin60° =30 sin60° =30 0.866025=25.98076 cm CBS: 60°60°60° CS=CB=15 cm  x=CB+AB/2+CS=15+30/2+15=45 cm

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