# Geometry/geometry

Advertisement

Question
In a 30degree 60degree 90degree triangle,the ratio of the length of the hypotenuse to the length of the shorter side is

Answer
Note that a 30-60-90 triangle is half of a triangle with equal angles and sides.
This makes the hypotenuse one of the sides of the triangle with the shorter leg as one of the sides.  Since that leg is half the hypotenuse, the length is 1/2  as much.  That makes the ratio be 2:1.

To say a little more, take the shorter side to be length 1.
This makes the hypotenuse be of length 2.
Since it is a right triangle, we know that 1² + s² = 2².
Since 2² = 4 and 1² = 1, that is 1 + s² = 4, so s = √3.
That is why I first remembered the sides of a 30-60-90 triangle to be as simple as 1-2-3.
What to remember is that the lengths are 1-2-√3 with 2 being on the hypotenuse.
Questioner's Rating
 Rating(1-10) Knowledgeability = 10 Clarity of Response = 10 Politeness = 10 Comment Thank you my daughter was right

• Add to this Answer
• Ask a Question

Geometry

All Answers

Answers by Expert:

Ask Experts

Volunteer

#### Scott A Wilson

##### Expertise

I can answer whatever questions you ask except how to trisect an angle. The ones I can answer include constructing parallel lines, dividing a line into n sections, bisecting an angle, splitting an angle in half, and almost anything else that is done in geometry.

##### Experience

I have been assisting people in Geometry since the 80's.

Education/Credentials
I have an MS at Oregon State and a BS at Oregon State, both with honors.

Awards and Honors
I was the outstanding student in high school in the area of geometry and math in general.

Past/Present Clients
Over 8,500 people, mostly in math, with almost 450 in geometry.

©2017 About.com. All rights reserved.

Browse Answers: