Answer: AB=√17, AD=√98,6
Step-by-step explanation:
AB²=BC²+AC²-2*BC*AC*cosACB
AB²=5²+4²-2*5*4*0,6=25+16-24=17
AB=√17
AD²=AC²+CD²-2*AC*CD*cosACD
cosACD=cos(180°-ACB)=-cosACB
AD²=4²+7²-2*4*7*(-0,6)=16+49+33,6=98,6
AD=√98,6
Answer:
The length of AB is 4.12cm and AD is 9.93cm
Using the formula, a²=b²+c²-2(b)(c)cosA to find the length :
cos ∠ACB = 0.6
∠ACB = 53.1° (1d.p)
c² = 5² + 4² - 2(5)(4)cos(53.1)
= 16.98 cm
c =√16.98
= 4.12 cm
AB = 4.12 cm
∠ACD = 180° - ∠ACB
= 180° - 53.1°
= 126.9°
c² = 7² + 4² - 2(7)(4)cos(126.9)
= 98.62 cm
c = √98.62
= 9.93 cm
AD = 9.93cm
