Question

a vertical flag pole TAD is supported by two wires AB and AC, given that angle ABD=67°,AB =2 m and AC =2.5m . find the length of AD​

Answer 1

a) 1.84m

b) 42.53°

Explanation:

First, look though the diagram provided by the question.

And use the formula:
`(a)/(sin A)=(b)/(sin B)=(c)/(sin C)`

Based on Additional Mathematics Form 4 (Dual Language Programme) KSSM from Malaysia

To find the length of AD

`(AD)/(sin 67)=(2)/(sin 90)`

`AD=(2)/(sin 90) * sin 67`

AD= 1.84 m

Find the angle C

`(sin 90)/(2.5)=(sin C)/(1.84)`

sin C=
`(sin 90)/(2.5) * 1.84`

= 0.736

`sin^(-1) (0.736)=47.39` degree

So, we have the value of AD and the value of angle C. Now , we can solve the the angle of CAD.

Same as the first question use the formula of sine rule and you will get the answer.

`(sin 90)/(2.5)=(sin ACD)/(1.69)`

`sinA = (sin90)/(2.5) * 1.69`

=0.676

=42.53°

So, the answer of the angle of CAD is 42.53°

Check the answer:

90°+47.39°+42.53°

=179.92°

=180°(rounded off)(Proved)

That is all from me. I hope you will understand my solution.