Homework Statement

What space the lengths of political parties NO and OP in triangle NOP?See the fastened figure

Homework Equations

The attempt at a Solution

Sorry i cant figure out how to attempt this question.Somebody please guide me exactly how to deal with it.Zulfi.

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Isn"t over there a ratio connected with similar triangles?Look in ~ the base. One is 40; the various other is 40+10.The ratio of bases is 40/50. Friend can apply that to other sides.
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Homework Statement

What are the lengths of political parties NO and OP in triangle NOP?See the fastened figure

Homework Equations

The difficulty doesn"t ask because that XP. It asks because that NO, the vertical next on the left, and also OP, the hypotenuse the the bigger triangle.

The effort at a Solution

Sorry ns cant number out exactly how to effort this question.Somebody please overview me how to settle it.Zulfi.
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First considering the "inner triangle" The tangent that the angle at ns is 24/40, i.e. Tan(angle in ~ P) = 24/40. So we know the tangent of that angle and that tangent needs to be the very same for the "outer triangle" together well. For this reason tan(angle in ~ P) = 24/40 = x/(40+10) or 24/40 = x/50. Solve for x and also you"ll have actually the length OP. So currently you have actually 2 political parties of a triangle and now it"s trivial to find the hypotenuse OP. (hint - Pythagorian theorem)
It"s much easier to usage the nature of similar triangles -- one can discover the size of top top without even writing something down. Trig isn"t required at all.
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It"s much much easier to use the nature of comparable triangles -- one can discover the size of ~ above without even writing noþeles down. Trig isn"t essential at all.
One that the beautiful things about Mathematics is that there are often several means of describing a problem or a solution and they indicate the exact same thing however each way can be unique enlightening, . In this situation I am using the properties of similar triangles simply as you suggest, specific the tangent is going to continue to be the same in both comparable triangles because the ratio of opposing and adjacent side of similar triangles will be the same. My systems doesn"t call for writing anything under or doing any trigonometry to with the answer. It just serves to illustrate why the property of similar triangles works, because the ratios between the lengths that sides stays the same.
Mod note: The write-up referred to below has been deleted for the reason provided here.This is coming an extremely close to a complete solution, i beg your pardon is something the PF helpers room forbidden. Informing the poster to usage "similar triangles" is one thing, however going with it step-by-step is something we are not claimed to do.
Mod note
: The write-up referred to below has been turned off for the reason provided here.This is coming very close come a finish solution, i beg your pardon is something the PF helpers space forbidden. Telling the poster to usage "similar triangles" is one thing, but going with it step-by-step is something we space not an alleged to do.

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Okay, fair enough. Mine bad. Ns came too close come an really solution. In retrospect might I rephrase and administer the hints "Consider whether or no the tangent of the angle at p is the same for both triangles and if for this reason what does the imply around the political parties of each triangle".In the future I"ll take care to offer helpful hints and also avoid explanations in which the limit of explanation approaches specific solution. :)
Hi,Thanks mine friends for your responses. I did not check the earlier close systems which has now been deleted. Very first i uncovered XP. Note X is a allude on the hypotnuse OP intersected through the altitude of smaller sized triangle and it was 46.64. After the i check out the write-up of magoo. Thanks to him. Then ns started reading the concept from the book and also i had the ability to make a following relationship: (Note AP is the base of smaller triangle, AX is the altitude and XP is the hypotenuse of smaller triangle.) SoOP/XP = NP/APOP/46.64 = 50/40OP = 58.3.Now (58.3)^2 = (50) ^2 + (NO)^2(NO)^2 = 898NO = 29.98Answers are correct.Thanks everybody.Zulfi.