Question

50 poin plus BeA ;-;​

Answer 1

Jawab:
Panjang AB = ¹³/₂(1+√3) cm

Penjelasan:
Diketahui ΔABC dengan
→ <A = 45°
→ <B = 30°
→ BC (sisi (a)) = 13 cm

Ditanya AB (sisi (c))
Cari <C
<A+<B+<C = 180
<C = 180-<A-<B
<C = 180-45-30
→ <C = 105°

Pake rumusan sinus
a/sin(<A) = c/sin(<C)
c = a×(sin(<C))÷(sin(<A))
c = 13×(sin(105°))÷(sin(45°))
c = 13×(sin(45+60°))÷(1÷√2)
c = (13√2) × (sin(45+60°))
∵ sin(p+q) = sin(p)cos(q) + sin(q)cos(p) ∴
c = (13√2) × (sin45cos60 + sin60cos45)
c = (13√2) × ((1÷√2)(1÷2) + ((√3)÷2)(1÷√2))
c = (13√2) × ((1÷(2√2)) + ((√3)÷(2√2)))
c = (13√2) × ((1+√3)÷(2√2))
c = [(13√2) ÷ (2√2)] × (1+√3) cm
c = ¹³/₂(1+√3) cm
Panjang AB = ¹³/₂(1+√3) cm
( xcvi )