Someone can help me with this problem?

[sebastian123]

 

[Dr.Peterson]

Sure. Where do you need help?

Please show whatever you have done, so we won't be duplicating effort. What similar triangles have you observed?

 

[sebastian123]

Sure. Where do you need help?

Please show whatever you have done, so we won't be duplicating effort. What similar triangles have you observed?

Well, I calculate P with the pythagorean theorem and then y calculate the sine with the trigonometric function θsine= Opposite/adjacent and I calculate the angle with the θarccosine

Then I calculate PA with opposite = θSin * hypothenuse


My result of the distance between PA is 4,615. but could you tell me if I am wrong in the answer?

 

[Dr.Peterson]

Your answer is correct; but you can get it much more easily, using similar triangles. Consider triangles BRO and POA.

As for your work: I don't know what it means to calculate P, since P is a point on a line; I would expect you to calculate the length of RO, and perhaps that is what you meant. And what angle did you calculate? Is θSin your notation for sin(θ)? It would have been better to show your actual work rather than a summary, so we could be sure of the details.

 

[pka]

Here is different approach using area.
We know that \(\Delta RBO\cong\Delta RAO\)
\(\text{area}(\Delta RBO)=\dfrac{5\cdot 12}{2}=30\).
Thus \(\text{area}(\Delta RAO)=\dfrac{P\cdot 13}{2}=30\). Now solve for \(P\).

 

[sebastian123]

Your answer is correct; but you can get it much more easily, using similar triangles. Consider triangles BRO and POA.

As for your work: I don't know what it means to calculate P, since P is a point on a line; I would expect you to calculate the length of RO, and perhaps that is what you meant. And what angle did you calculate? Is θSin your notation for sin(θ)? It would have been better to show your actual work rather than a summary, so we could be sure of the details.

 

[Dr.Peterson]

Using the similar triangles I suggested, we bypass the trigonometry: RO = 13, so comparing POA to BRO, we have x/12 = 5/13, leading immediately to x = 12*5/13 = 60/13 = 4.6153846... . That's because your sin(POA) = sin(BRO) = opp/hyp = 12/13, without needing a calculator.

And pka, of course, got the same result by areas (but you were told to use similar triangles).