Pertanyaan

Pada sebuah segitiga K L M , dengan siku-siku di L , jika sin M = 3 2 dan panjang sisi KL = 10 cm, tentukan panjang sisi segitiga yang lain dan nilai perbandingan trigonometri lainnya

Pada sebuah segitiga $K L M$ , dengan siku-siku di $L$ , jika $sin M = \frac{2}{3}$ dan panjang sisi KL = 10 cm, tentukan panjang sisi segitiga yang lain dan
nilai perbandingan trigonometri lainnya

A. Pusporini

Master Teacher

Jawaban terverifikasi

Pembahasan

Rumus Dasar Trigonometri Diketahui segitiga , dengan siku-siku di . Panjang cm dan . sehingga, panjang sisi segitiga adalah cm; cm; dan cm. Jika maka perbandingan trigonometri

Rumus Dasar Trigonometri

$begin mathsize 14px style table row cell sin space M equals fraction numerator d e over denominator m i end fraction semicolon end cell cell cos e c space M equals fraction numerator m i over denominator d e end fraction end cell row cell cos space M equals fraction numerator s a over denominator m i end fraction semicolon end cell cell s e c space M equals fraction numerator m i over denominator s a end fraction end cell row cell tan M beta equals fraction numerator d e over denominator s a end fraction semicolon end cell cell c o t space M equals fraction numerator s a over denominator d e end fraction space end cell end table end style$

Diketahui segitiga , dengan siku-siku di .

Panjang cm dan .

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sin space M end cell equals cell fraction numerator K L over denominator K M end fraction end cell end table end style$

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 over 3 end cell equals cell fraction numerator 10 over denominator K M end fraction end cell row cell 2 times K M end cell equals cell 10 times left parenthesis 3 right parenthesis end cell row cell 2 times K M end cell equals 30 row cell K M end cell equals cell 30 over 2 end cell row cell K M end cell equals cell 15 space c m end cell end table end style$

sehingga, panjang sisi segitiga adalah cm; cm; dan cm.

Jika maka perbandingan trigonometri

$begin mathsize 14px style cos space M equals fraction numerator L M over denominator K M end fraction equals fraction numerator 5 square root of 5 over denominator 15 end fraction equals fraction numerator square root of 5 over denominator 3 end fraction end style$
$begin mathsize 14px style tan space M equals fraction numerator K L over denominator L M end fraction equals fraction numerator 10 over denominator 5 square root of 5 end fraction equals fraction numerator 2 over denominator square root of 5 end fraction times fraction numerator square root of 5 over denominator square root of 5 end fraction equals fraction numerator 2 square root of 5 over denominator 5 end fraction end style$
$begin mathsize 14px style cos e c space M equals fraction numerator K M over denominator K L end fraction equals 15 over 10 equals 3 over 2 end style$
$begin mathsize 14px style s e c space M equals fraction numerator K M over denominator L M end fraction equals fraction numerator 15 over denominator 5 square root of 5 end fraction equals fraction numerator 3 over denominator square root of 5 end fraction times fraction numerator square root of 5 over denominator square root of 5 end fraction equals fraction numerator 3 square root of 5 over denominator 5 end fraction end style$
$begin mathsize 14px style c o t space M equals fraction numerator L M over denominator K L end fraction equals fraction numerator 5 square root of 5 over denominator 10 end fraction equals fraction numerator square root of 5 over denominator 2 end fraction end style$