Question

Find the length of the side AB in the triangle ∆ABC in the figure Find the length of the side AB in the triangle ∆ABC in the figure @Mathematics

Answer 1

Use sine law to find angle B
180 - angle B - angle A = angle C
Use cosine law to find side c

Answer 2

sin 122 / 10 = sin (angle B) / 5
solve for angle B first

Answer 3

cosine rule is

10^2 = c^2 + 5^2 - 2*c*5 cos 122
solve for c

Answer 4

10^2=c^2+25-10ccos122

Answer 5

100=c^2+15ccos122

Answer 6

hello, I have a test on tue and we are working with triangels also.

Answer 7

u have a quadratic in c:
c^2 +15cos122 c - 100 = 0
cos 122 = -0.53 so
c^2 - 7.95c - 100 = 0

solve this using the quadratic formula
the positive root will be the length of AB

Answer 8

i have to factor it for quadratic right? i dont really remember how to do it.

Answer 9

hold on thats wrong

Answer 10

ok.

Answer 11

100=c^2+15ccos122 is incorrect

10^2=c^2+25-10ccos122 is correct

this gives

c^2 - 10cos122 c - 75 = 0
c^2 + 5.3c - 75 = 0
this cant be factorised
you can use the formula

x = [-b =- sqrt(b^2-4ac) ] / 2a

where a = 1, b = 5.3 and c = -75

Answer 12

but that isnt any of the choices.

Answer 13

what are the choices?

Answer 14

c= 6.39
c=7.39
c=6.64
c=6.89
c=7.14

Answer 15

ok - work out the way i said and youll get close to 6.39 - i got 6.4 - maybe the 5.3 was nt quite accurate enough

your answer is 6.39