Roboguru

Diketahui segitiga  siku-siku di  dengan panjang sisi . Jika , tentukanlah panjang sisi  dan !

Pertanyaan

Diketahui segitiga begin mathsize 14px style A B C end style siku-siku di begin mathsize 14px style B end style dengan panjang sisi begin mathsize 14px style A C equals 6 square root of 2 space cm end style. Jika begin mathsize 14px style angle B A C equals 45 degree end style, tentukanlah panjang sisi begin mathsize 14px style A B end style dan begin mathsize 14px style B C end style!

Pembahasan Soal:

Diketahui segitiga begin mathsize 14px style A B C end style siku-siku di begin mathsize 14px style B end style dengan panjang sisi begin mathsize 14px style A C equals 6 square root of 2 space cm end style dan begin mathsize 14px style angle B A C equals 45 degree end style, jika digambarkan adalah:



Akibatnya panjang begin mathsize 14px style A B equals B C end style. Dimisalkan begin mathsize 14px style A B equals B C equals x end style, maka didapatkan:

size 14px x to the power of size 14px 2 size 14px plus size 14px x to the power of size 14px 2 blank size 14px equals begin mathsize 14px style left parenthesis 6 square root of 2 right parenthesis end style to the power of size 14px 2 size 14px x to the power of size 14px 2 size 14px plus size 14px x to the power of size 14px 2 size 14px equals size 14px 6 to the power of size 14px 2 size 14px cross times size 14px left parenthesis square root of size 14px 2 size 14px right parenthesis to the power of size 14px 2 size 14px 2 size 14px x to the power of size 14px 2 size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px equals size 14px 72 size 14px x to the power of size 14px 2 size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px equals size 14px 72 over size 14px 2 size 14px x to the power of size 14px 2 size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px equals size 14px 36 size 14px x size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px equals square root of size 14px 36 size 14px x size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px equals size 14px plus-or-minus size 14px 6

Karena panjang sisi tidak mungkin negatif maka panjang sisi begin mathsize 14px style A B equals 6 space cm space dan space B C equals 6 space cm end style.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 20 Mei 2021

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