Relative velocity question from giancoli physics

[hamsterpower7]

Homework Statement

I attached the picture on the bottom (correction on the picture 30 degrees ---> 35 degrees sorry about that)
Vpa: 600 km/h
Vag:100 km/h

and the question is to find the angle theta

Homework Equations

The Attempt at a Solution

So I tried using Pythagorean theory by setting x and y

$$(V_pa)^2 =y^2 + x^2$$

set $$y = x/ (tan 35)$$

so then I solved x = 344.1458617 Km/h

and since $$Sin/theta = (V_ag + x)/V_pa$$

$$/theta = 47.75271609$$

sorry for ignoring the scientific notation,
I am not used to it :(

um anyways my answer was wrong
because the "solution" chose to use the 'sine law'
and that gives the right answer but I wanted to know what I did wrong to get the wrong answermuch appreciated

 

[PeterO]

Homework Statement

I attached the picture on the bottom (correction on the picture 30 degrees ---> 35 degrees sorry about that)
Vpa: 600 km/h
Vag:100 km/h

and the question is to find the angle theta

Homework Equations

The Attempt at a Solution

So I tried using Pythagorean theory by setting x and y

$$(V_pa)^2 =y^2 + x^2$$

set $$y = x/ (tan 35)$$

so then I solved x = 344.1458617 Km/h

and since $$Sin/theta = (V_ag + x)/V_pa$$

$$/theta = 47.75271609$$

sorry for ignoring the scientific notation,
I am not used to it :(

um anyways my answer was wrong
because the "solution" chose to use the 'sine law'
and that gives the right answer but I wanted to know what I did wrong to get the wrong answer


much appreciated

Your diagram shows right angled triangles. The real situation may not be right angled, which would necessitate use of sin rule or cos rule

 

[hamsterpower7]

Okay I will post the question up to see if it wasn't a right angle

An airplane, whose air speed is 600km/h, is supposed to fly in a straight path 35 degrees north of east
but a steady 100km/h wind is blowing from the north
in what direction shuold the plane head?

 

[PeterO]

Homework Statement

I attached the picture on the bottom (correction on the picture 30 degrees ---> 35 degrees sorry about that)
Vpa: 600 km/h
Vag:100 km/h

and the question is to find the angle theta

Homework Equations

The Attempt at a Solution

So I tried using Pythagorean theory by setting x and y

$$(V_pa)^2 =y^2 + x^2$$

set $$y = x/ (tan 35)$$

so then I solved x = 344.1458617 Km/h

and since $$Sin/theta = (V_ag + x)/V_pa$$

$$/theta = 47.75271609$$

sorry for ignoring the scientific notation,
I am not used to it :(

um anyways my answer was wrong
because the "solution" chose to use the 'sine law'
and that gives the right answer but I wanted to know what I did wrong to get the wrong answer


much appreciated

[Responding to your original so I can copy your symbols]

Your first line was incorrect

$$(V_pa)^2 =y^2 + x^2$$

It should read

$$(V_pg)^2 =y^2 + x^2$$

and since you don't know $$(V_pg)$$ it doesn't get you anywhere.

You have to use the sine rule on the triangle including theta to solve