Centre of the hypotenuse

For 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 sinα=CBAB sinβ=ACAB  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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