2/3 Dimensional Trig problem

[Alexeia]

Hi,

I have tried, but failed to solve question 4.2.2 and 4.2.3 of the exercise problem. Any help please!!

4.2: In the diagram, P, Q, and R are points on the same horizontal plane. WP is a vertical telephone mast. The angle of elevation from W to Q is \(\displaystyle \, \alpha.\,\) \(\displaystyle \angle PQR\, =\,y,\, \angle PRQ\, =\, x,\, \) and \(\displaystyle QR\, =\, 15\,\) meters.

4.2.1: Express PW in terms of PQ and \(\displaystyle \,\alpha.\)

4.2.2: Hence, show that \(\displaystyle \, PR\, =\, \dfrac{15\, \sin(y)}{\sin(x\, +\, y)}\)

4.2.3: If x = y, show that \(\displaystyle \, PW\, =\, 7.5\, \dfrac{\tan(\alpha)}{\cos(y)}\)

I tried to use the sine rule and cosine rule but can't get side PR.

Thanks,
Alexeia

 

[Deleted member 4993]

Hi,


I have tried, but failed to solve question 4.2.2 and 4.2.3 of the exercise problem.


Any help please!!


I tried to use the sine rule and cosine rule but can't get side PR.


Thanks,
Alexeia

What did you get for 4.2.1?

Do you know the Law of Sines for triangles?

If you do - please state for triangle PRQ.

If not - look up in your text-book or Google - and then please state for triangle PRQ.

 

[Alexeia]

I got:

4.2.1 PW = PQ.tan(∝)

4.2.2 PQ/sin(x) =PR/sin(y) (/ means fraction e.g. PQ over sinx)

 

[Deleted member 4993]

I got:

4.2.1 PW = PQ.tan(∝)

4.2.2 PQ/sin(x) =PR/sin(y) (/ means fraction e.g. PQ over sinx)

Let angle QPR = Θ

Then Θ + x + y = 180° → Θ = 180° - (x + y)

Also

PQ/sin(x) = PR/sin(y) = 15/sin(Θ)

Now continue....

 

[Alexeia]

thanks, I got it right!!