Triangle's 9731

Solve the triangle ABC if the side a = 52 cm, the height on the other side is vb = 21 cm, and the triangle's area is S = 330 cm2.

Correct answer:

b =  31.4286 cm
c1 =  25.1992 cm
c2 =  -25.1992 cm

Step-by-step explanation:

a=52 cm v2=21 cm S=330 cm2  S=2b v2  b=2 S/v2=2 330/21=7220 cm=31.4286 cm
S=s (sa)(sb)(sc) s=(a+b+c)/2=a/2+b/2+c/2  S=(a/2+b/2+c/2) (a/2+b/2+c/2a)(a/2+b/2+c/2b)(a/2+b/2+c/2c) S=(a/2+b/2+c/2) (b/2+c/2a/2)(a/2+c/2b/2)(a/2+b/2c/2) 330330=(a/2+b/2+c/2)(b/2+c/2a/2)(a/2+c/2b/2)(a/2+b/2c/2)  330 330=(52/2+31.428571428571/2+c/2) (31.428571428571/2+c/252/2) (52/2+c/231.428571428571/2) (52/2+31.428571428571/2c/2) 461.406888c2+292993.534=0 461.406888c2292993.534=0  p=461.406888;q=0;r=292993.534 D=q24pr=024461.406888(292993.534)=540756939.57395 D>0  c1,2=2pq±D=922.813776±540756939.57 c1,2=±25.199213237863 c1=25.199213237863=25.1992 cm c2=25.199213237863   Factored form of the equation:  461.406888(c25.199213237863)(c+25.199213237863)=0  c=26.487 cm c=25.199 cm  s=(a+b+c)/2=(52+31.4286+25.199)/254.3138 cm S1=s (sa) (sb) (sc)=54.3138 (54.313852) (54.313831.4286) (54.313825.199)289.3683 cm2 S1=S

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