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# Don't understand part of the answer (Pythagoras, Trigonometry, Triangles)

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1. Howdy.

I am working on a past paper and I have written the answers from the mark scheme down. http://imgur.com/7vrvguW

Can someone explain what is going on please?

I see we start off by using Pythagoras to find AC and DA.

But why are we finding the angles BAC and DAC?

Then it uses the sum of the angles, multiplied by sin and also SQRT(5^2 +2^2).

Thanks
2. (Original post by makin)
But why are we finding the angles BAC and DAC?
Notice that triangle DAP is a right angled triangle. So one can use SOHCAHTOA to say that:

And after a bit of basic rearranging, we can see that . So, it's clear that if we can figure out the length AD and the angle DAP, then we can plug those in to the right hand side up there and find DP (which is what you've been asked to find in the first place).

So now the question breaks down into two chunks:

(1) Find Angle DAP

Notice that one way to find angle DAP is to find angles BAC and DAC and add them together - so, to answer your first question, this means that angle BAC and angle DAC are found in order to find angle DAP.

Then it uses the sum of the angles, multiplied by sin and also SQRT(5^2 +2^2)
Notice the formula we found up there for the length DP. See the similarity?

Careful, by the way, that quantity is NOT "the sum of the angles multiplied by sin" - that is 'the sine of the sum of the angles'. Multiplying something by "sin" is meaningless unless it's sin(of something), as sin in it's own right is not a quantity.
3. (Original post by Farhan.Hanif93)
Notice that triangle DAP is a right angled triangle. So one can use SOHCAHTOA to say that:

And after a bit of basic rearranging, we can see that . So, it's clear that if we can figure out the length AD and the angle DAP, then we can plug those in to the right hand side up there and find DP (which is what you've been asked to find in the first place).

So now the question breaks down into two chunks:

(1) Find Angle DAP

Notice that one way to find angle DAP is to find angles BAC and DAC and add them together - so, to answer your first question, this means that angle BAC and angle DAC are found in order to find angle DAP.

Notice the formula we found up there for the length DP. See the similarity?

Careful, by the way, that quantity is NOT "the sum of the angles multiplied by sin" - that is 'the sine of the sum of the angles'. Multiplying something by "sin" is meaningless unless it's sin(of something), as sin in it's own right is not a quantity.
Thanks for taking the time to help me. I fully understand what is going on now

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