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- agha79
- Students
- Posts: 3
- Joined: Mon Aug 29, 2011 3:57 am
OG Page 260 Problem 8 and 9
i have no idea how to draw pictures so please can someone walk me through question 8 and 9 at page 260 of official guide?
- tommywallach
- Manhattan Prep Staff
- Posts: 1917
- Joined: Thu Mar 31, 2011 11:18 am
Re: OG Page 260 Problem 8 and 9
Hey Agha,
For #8, the key is to recognize that these are similar triangles. Similar triangles are any triangles with the same angle measurements. We know these two are similar, because they are both right triangles (so they both have one angle that's = 90 degrees), they share angle P, and their third angles are along the same line (PO). This means that the ratio between the sides is always the same.
This allows us to solve directly for NO using ratios 24/40 (the ratio of base to height in the smaller triangle) = x/50 (the ratio of base to height in the larger triangle). So x = 30.
Then we can just use pythagoras to solve for PO. PO^2 = Square root (50 ^ 2 + 30 ^2).
Make sense?
-t
For #8, the key is to recognize that these are similar triangles. Similar triangles are any triangles with the same angle measurements. We know these two are similar, because they are both right triangles (so they both have one angle that's = 90 degrees), they share angle P, and their third angles are along the same line (PO). This means that the ratio between the sides is always the same.
This allows us to solve directly for NO using ratios 24/40 (the ratio of base to height in the smaller triangle) = x/50 (the ratio of base to height in the larger triangle). So x = 30.
Then we can just use pythagoras to solve for PO. PO^2 = Square root (50 ^ 2 + 30 ^2).
Make sense?
-t
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