Pertanyaan

Perhatikan gambar berikut. Sebuah pohon dilihat dari dua tempat berbeda, yaitu A dan B. Jarak AB = 30 m . Hitunglah tinggi pohon tersebut.

Perhatikan gambar berikut. Sebuah pohon dilihat dari dua tempat berbeda, yaitu A dan B. Jarak $AB = 30 m$ . Hitunglah tinggi pohon tersebut.

F. Ayudhita

Master Teacher

Jawaban terverifikasi

Jawaban

tinggi pohon = .

tinggi pohon =

Pembahasan

Perhatikan segitiga BCD Lalu Perhatikan segitiga ACD Jadi tinggi pohon = .

Perhatikan segitiga BCD

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell tan space 45 to the power of ring operator end cell equals cell fraction numerator C D over denominator B C end fraction end cell row 1 equals cell fraction numerator C D over denominator B C end fraction end cell row cell B C end cell equals cell C D end cell end table end style$

Lalu

Perhatikan segitiga ACD

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell tan space 30 to the power of ring operator end cell equals cell fraction numerator C D over denominator A C end fraction end cell row cell fraction numerator 1 over denominator square root of 3 end fraction end cell equals cell fraction numerator C D over denominator 30 plus C D end fraction end cell row cell 30 plus C D end cell equals cell C D square root of 3 end cell row 30 equals cell C D square root of 3 minus C D end cell row 30 equals cell C D open parentheses square root of 3 minus 1 close parentheses end cell row cell C D end cell equals cell fraction numerator 30 over denominator open parentheses square root of 3 minus 1 close parentheses end fraction times fraction numerator open parentheses square root of 3 plus 1 close parentheses over denominator open parentheses square root of 3 plus 1 close parentheses end fraction end cell row cell C D end cell equals cell fraction numerator 30 open parentheses square root of 3 plus 1 close parentheses over denominator open parentheses square root of 3 close parentheses squared minus 1 squared end fraction end cell row cell C D end cell equals cell fraction numerator 30 open parentheses square root of 3 plus 1 close parentheses over denominator 3 minus 1 end fraction end cell row cell C D end cell equals cell 15 open parentheses square root of 3 plus 1 close parentheses space straight m end cell end table end style$

Jadi tinggi pohon = .