Question

Find size of angle ABC

Answer 1

Then find length of AD

Answer 2

I used cosine rule:
b^2=a^2 + c^2 - 2ac cosB
11.4^2 = 5.7^2 + 7.6^2 -(2*5.7*7.6*cosB)
129.96-32.49-57.76 = -86.64*cosB
cosB = -(39.71/86.64)
B = 117.28

Answer 3

Then used sine rule to find angle A as 63.62

Answer 4

No, sorry, A = 26.38

Answer 5

Therefore angle ACD = 90 - 26.38 = 63.62

Answer 6

So using sine rule, sin CAD/CD = sin D/AC

sin 63.62/CD = sin 90/11.4
CD sin 90 = 11.4 sin 63.62
CD = 11.4 sin 63.62/sin 90
CD = 10.2

Answer 7

Could someone check this is correct? Thanks so much :-)

Answer 8

Angle ACD in step 5 should read angle CAD

Answer 9

if u have got angle a...u can use SOH CAH TOA..u will get length AD

Answer 10

Oh, that's much easier! So angle A = 26.58, hypotenuse is 11.4, and AD is adjacent, so
cos26.58 = AD/11.4
AD = 11.4 cos 26.58
AD = 10.2

Thanks, I didn't spot that

Answer 11

But other than that, do you agree with my answer?

Answer 12

yepz u amswer is completely right...bu to save time for exams,u can use my method