1.Nilai cos 30° + sin² 45° + tan 60°/sec 60°.tan 45° a.1/4 (3√3 + 1) b.1/2 (3√3 + 1) c.1/4 (√3 + 1 ) d.1/2 (√3 + 1 ) e.3√3 + 1 2.Di ketahui segitiga MAB dengan
Matematika
IOwl
Pertanyaan
1.Nilai cos 30° + sin² 45° + tan 60°/sec 60°.tan 45°
a.1/4 (3√3 + 1)
b.1/2 (3√3 + 1)
c.1/4 (√3 + 1 )
d.1/2 (√3 + 1 )
e.3√3 + 1
2.Di ketahui segitiga MAB dengan AB = 30 cm , sudut A = 60°,dan sudut B = 75°.Nilai AM =
a.15(1 +√3)
b.15(√2+√3)
c.15(3 + √3)
d.15(√2+√6)
e.15(√3+√6)
a.1/4 (3√3 + 1)
b.1/2 (3√3 + 1)
c.1/4 (√3 + 1 )
d.1/2 (√3 + 1 )
e.3√3 + 1
2.Di ketahui segitiga MAB dengan AB = 30 cm , sudut A = 60°,dan sudut B = 75°.Nilai AM =
a.15(1 +√3)
b.15(√2+√3)
c.15(3 + √3)
d.15(√2+√6)
e.15(√3+√6)
2 Jawaban
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1. Jawaban alvinteguh
1. (cos 30 + sin²45 + tan 60)/(sec 60 . tan 45)
= (1/2 √3 + (1/2 √2)² + √3)/(1/cos 60 . 1)
= (1/2 √3 + 1/4 . 2 + √3)/(1/(1/2))
= (3/2 √3 + 1/2)/2
= 3/4 √3 + 1/4
= 1/4 (3√3 + 1)
2. < M = 180° - 60° - 75° = 45°
pertama gunakan aturan sinus
AB/sin M = BM/sin A
30/sin 45 = BM/sin 60
30/(1/2 √2) = BM/(1/2 √3)
coret 1/2 nya
30/√2 = BM/√3
30√3 = √2 BM
BM = 30√3/√2
BM = 30√3/√2 . √2/√2
BM = 30√6/2 = 15√6 cm
lalu gunakan aturan cosinus
cos A = (AM² + AB² - BM²)/(2 . AM . AB)
cos 60 = (AM² + 30² - (15√6)²)/(2 . AM . 30)
1/2 = (AM² + 900 - 1350)/(60 AM)
1/2 = (AM² - 450)/(60 AM)
60 AM = 2 AM² - 900
0 = 2 AM² - 60 AM - 900
karena tidak bisa difaktorkan maka gunakan rumus ABC
AM = (-(-60) + √((-60)² - 4 . 2(-900))/(2 . 2)
AM = (60 + √(3600 + 7200))/4
AM = 15 + 1/4 √(10800)
AM = 15 + 1/4 . √3600 . √3
AM = 15 + 1/4 . 60 . √3
AM = 15 + 15√3
AM = 15(1 + √3) cm -
2. Jawaban whongaliem
1) (cos 30° + sin² 45° + tan 60° ) / (sec 60° tan 45°)}
= { (1/2√3) + (1/2√2)² + (√3)} / (2 . 1) }
= { 1/2 √3 + 1/2 + √3 } / 2
= {(3/2)√3 + 1/2 } / 2
= (3/4)√3 + 1/4
= (1/4) (3√3 + 1) ..... jawaban : A
2) sin 75° = sim (30° + 45°)
= sin 30° .cos 45° + cos 30° .sin 45°
= 1/2 . 1/2 √2 + 1/2 √3 . 1/2 √2)
= 1/4 (√2 + √6)
∠ M = 180° - 60° - 75°
= 45°
AM / sin B = AB / sin M
AM / sin 75° = 30 / sin 45°
AM / {1/4 (√2 + √6) = 30 / (1/2√2)
4.AM / (√2 + √6) = 60/√2
4√2 AM = 60 (√2 + √6)
AM = 60 (√2 + √6) / 4√2
AM = 15 (√2 + √6) / √2
AM = 15/2 (2 + √12)
AM = 15/2 (2 + 2√3)
AM = 15/2 . 2 (1 + √3)
AM = 15 (1 + √3) ..... jawaban : A