# Thread: How do I solve this?

1. ## How do I solve this?

The question reads Calculate the Length of PS

2. Originally Posted by iamanoobatmath
The question reads Calculate the Length of PS

Is the entire length of QR 10 cm?

3. Yes

4. Hello,

Originally Posted by iamanoobatmath
The question reads Calculate the Length of PS

You can see that $\displaystyle 55+35=90$

Therefore, PQR is a right angle triangle at P.

So now, use trigonometry, for example :

In triangle PQR :
$\displaystyle \cos 55=\frac{PQ}{10} \implies PQ=\dots$

Then, in triangle PQS, $\displaystyle \sin 55=\dots$

6. Originally Posted by iamanoobatmath
The question reads Calculate the Length of PS

First notice that $\displaystyle P = 90$ degrees

Use the Sin Rule

$\displaystyle \frac{Sin P}{p} = \frac{Sin Q}{q}$

$\displaystyle \frac{Sin 90}{10} = \frac{Sin 55}{q}$

$\displaystyle q = 8,1915 = PR$

$\displaystyle Sin 35 = \frac{PS}{PR} = \frac{PS}{8,1915}$

$\displaystyle PS = (8,1915) \times sin 35 = 4,6985$ approx.

7. Originally Posted by iamanoobatmath
Some special relations in this case: $\displaystyle \overline{PQ}^{2}=\overline{QS}\cdot \overline{QR},\,\overline{PR}^{2}=\overline{RS}\cd ot \overline{RQ},\,\overline{PS}^{2}=\overline{SQ}\cd ot \overline{SR}.$