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

Answer:

a) 1.84m

b) 42.53°

Step-by-step explanation:

First, look though the diagram provided by the question.

And use the formula: $\frac{a}{sin A}=\frac{b}{sin B}=\frac{c}{sin C}$

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

To find the length of AD

$\frac{AD}{sin 67}=\frac{2}{sin 90}$

$AD=\frac{2}{sin 90} * sin 67$

AD= 1.84 m

Find the angle C

$\frac{sin 90}{2.5}=\frac{sin C}{1.84}$

sin C=$\frac{sin 90}{2.5} * 1.84$

= 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.

$\frac{sin 90}{2.5}=\frac{sin ACD}{1.69}$

$sinA = \frac{sin90}{2.5} * 1.69$

=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.