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Pertanyaan

Perhatikan segitiga siku-siku ABC di bawah.

Tentukan:

a. keliling segitiga ABC.

R. Septa

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

keliling segitiga ABC adalah begin mathsize 14px style 48 plus 2 square root of 217 space cm end style.

Pembahasan

Jumlah sudut segitiga begin mathsize 14px style equals 180 degree end style.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell angle straight A plus angle straight B plus angle straight C end cell equals cell 180 degree end cell row cell angle straight A plus 30 degree plus 90 degree end cell equals cell 180 degree end cell row cell angle straight A plus 120 degree end cell equals cell 180 degree end cell row cell angle straight A end cell equals cell 60 degree end cell end table end style  

Dengan menerapkan definisi tangen.

undefined   

Panjang begin mathsize 14px style AB equals 8 space cm plus 24 space cm equals 32 space cm end style.

Dengan Pythagoras kita dapat

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row AC equals cell square root of AD squared plus CD squared end root end cell row AC equals cell square root of 8 squared plus open parentheses 8 square root of 3 close parentheses squared end root end cell row AC equals cell square root of 64 plus 192 end root end cell row AC equals cell square root of 256 end cell row AC equals cell 16 space cm end cell end table end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row BC equals cell square root of BD squared plus CD squared end root end cell row BC equals cell square root of 24 squared plus open parentheses 8 square root of 3 close parentheses squared end root end cell row BC equals cell square root of 576 plus 192 end root end cell row BC equals cell square root of 868 end cell row BC equals cell 2 square root of 217 space cm end cell end table end style 

Sehingga kelilingnya adalah

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell Keliling space ABC end cell equals cell AB plus BC plus AC end cell row blank equals cell 32 plus 2 square root of 217 plus 16 end cell row blank equals cell 48 plus 2 square root of 217 space cm end cell end table end style 

Jadi, keliling segitiga ABC adalah begin mathsize 14px style 48 plus 2 square root of 217 space cm end style.

22

3.3 (3 rating)

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