If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

### Course: High school geometry>Unit 5

Lesson 4: Ratios in right triangles

# Using similarity to estimate ratio between side lengths

When two right triangles share an acute angle measure, the ratios of the corresponding side lengths within the triangles are equal.  Created by Sal Khan.

## Want to join the conversation?

• Is there a easier way to do this? There are questions on the practice that Sal does not explain. Maybe cousin Fal could explain to me.
• There actually is another way to do this! If you remember the angle-angle similarity, then you would know that the triangle PNM is similar to the triangle 2 as they both have a right angle and an angle of 90°. because of that, PN(opposite)/MN(adjacent) = 5.7(opposite)/8.2(adjacent).
• At what did Sal mean when he said "We can take the ratio across triangles"?
• It just means you can create a ratio (think of it in fraction form) of similar sides from one triangle to the other.
• so, since all of the angles added together have to equal 180 and there is always one 90 degree angle, can one angle be like 89 degrees and the other 1 degree or is that not how this works?
• That's absolutely how this works. A 1-89-90 triangle would be very long and narrow, but still be a valid triangle.
• At , why did Sal choose triangle 2 to approximate the ratio of PN over MN and not triangle 1 or triangle 3 to approximate the ratio of PN over MN?
• For similar triangles, the angles must be the same. So triangle 2 matches the 35-55-90 angles.
• does the square let you know it's a right angle ?
• yes it is a symbol for 90 degrees.
• How did Sal know which triangle to use?
I got lost when he was talking about which triangle to choose for the problem.
• The Triangle we need to find the ratio for had two angles. Of those two angles one being 90, which all three of the other triangles shared. The second angle, which was 35, was only found on one other triangle, and since all triangles have to have their angles add up to 180 we can asume that the triangle we are working with and the triangle that had 35 degrees both have the exact same angles. As such their ratios must be the same.
• I think Sal could make a really good book narrator, especially in one of those calming adult books. He'd narrate good calming go-to sleep type of book for adults well.
• Can someone help? there are a few questions on the practice that Sal does not explain. I really need help with this And i don't really understand how to do this.