How to find the hypotenuse in a right-angled triangle
Geometry is not an easy science. It requires special attention and knowledge of exact formulas. This kind of mathematics came to us from Ancient Greece and even after several thousand years it does not lose its relevance. Do not be in vain to think that this is a useless thing, hammering the head of students and schoolchildren. In fact, geometry is applicable in many spheres of life. Without it, knowledge of geometry does not build any architectural structure, do not create cars, spacecraft and aircraft. Complex and not very highways and road interchanges - this all needs geometric calculations. Yes, even sometimes you can not do repairs in your room without knowing the elementary formulas. So do not underestimate the importance of this subject. The most frequent formulas that have to be used in many solutions, we study in school. One of them is finding the hypotenuse in a right-angled triangle. To understand this, read below.
Before starting practice, let's start with the basics and determine what a hypotenuse is in a right-angled triangle.
Hypotenuse is one of the sides in a right-angled triangle that is opposite the angle of 90 degrees (right angle) and is always the longest.
There are several ways to find the length of the desired hypotenuse in a given rectangular triangle.
In the case when the legs are already known, we use the Pythagorean theorem, where we add the sum of the squares of the two legs, which will be equal to the square of the hypotenuse.
a and b -cathets, c-hypotenuse.
In our case, for a right-angled triangle, respectively, the formula is as follows:
If we substitute the known numbers of a and b, let it be a = 3 and b = 4, then c = √32 + 42, then we get c = √25, c = 5
When we know the length of only one leg, the formula can be transformed to find the length of the second. It looks like this:
In the case when, according to the conditions of the problem, we know the cathetet A and the hypotenuse C, then we can calculate the right angle of the triangle, let's call it α.
To do this, we use the formula:
Let the second angle, which we need to calculate, be β. Given that we know the sum of the angles of the triangle, which is 180 °, then: β = 180 ° -90 ° -α
In the case when we know the values of the legs, we can use the formula to find the value of the acute angle of the triangle:
Depending on the known generally accepted values, the sides of the rectangle can be found by the set of different formulas. Here are some of them:
When solving problems with finding unknowns inrectangular triangle, it is very important to focus on the values already known to you and, based on this, to substitute them in the desired formula. Immediately remember them will be difficult, so we advise you to make a small hand-written hint and paste it into the notebook.
As you can see, if you delve into all the subtleties of thisformula, then you can easily figure it out. We recommend trying to solve several problems based on this formula. After you see your result, you will become clear if you understand this topic or not. Try not to memorize, but to delve into the material, it will be much more useful. The jagged material is forgotten after the first test, and this formula will occur to you quite often, so first understand it, and then memorize it. If these recommendations did not have a positive effect, then there is a sense in additional lessons on this topic. And remember: learning is light, and not learning is darkness!
