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### Course: High school geometry>Unit 5

Lesson 4: Ratios in right triangles

# Using right triangle ratios to approximate angle measure

Because of similarity, all right triangles with a given acute angle measure have equal ratios between their side lengths. So if we know two of the side lengths of a right triangle, we can figure out the angle measures, too! Created by Sal Khan.

## Want to join the conversation?

• Hi, I don't understand why Sal uses opposite leg length/hypotenuse length. Shouldn't it be adjacent length/ hypotenuse length? Can you help me, thx.
• He could have used it but you see we only have the value of opposite side and the hypotenuse. So in order to figure out the ratio he went on with opposite over hypotenuse
• How do you know the difference between the adjacent and the opposite leg length?
I always get confused with these two names.
• It appears that you can pick out the hypotenuse (longest side opposite the 90 degree angle). Adjacent means next to (like two rooms with a door between them, you walk right in). This forms the reference angle with the hypotenuse. Opposite would be like having to walk across a hall before going in the room, so if you start at the reference angle, you have to walk through the middle of the triangle to find the opposite side.
• What is the significance of the 'm' in m∠D?
• It's short for 'measure'. ∠D is the actual angle D, the geometric plane figure. m∠D is the measure of the angle, which is a number like 25º.
• what is a 'leg'? at ? THANKS
• A leg of a right triangle is a side other than the hypotenuse. The triangle has one hypotenuse and two legs.

We also use the term for isosceles triangles; a leg is one of the pair of congruent sides.
• ion even know what happening
• what is a hypotenuse or a adjacent length? thanks.
(1 vote)
• Hypotenuse is always the longest side of a right triangle across from the 90 degree angle. One of the two acute angles will be a reference angle, so adjacent side forms the reference angle with the hypotenuse. The opposite side requires you to go through the middle of the triangle from the reference angle.
• I thought that to find the angle, we needed to use the ratio of the two sides connected to the vertex, but Sal uses the Opposite and Hypotonuse. While I used Pythagroums Therom to find the Adjacent side and then used the a/h ratio to solve. Would Sal's way work for all triangles similar to his or did he only do it based on that specific triangle? I really appreciate any help you can provide.
• Trig functions allow us to find both the acute angles of a right triangle no matter which of the sides we have. It will work as long as it is a right triangle. The problem with going through two steps is that you may end up rounding the first time which could throw the answer off some by having to use a rounded answer.