What is Signified by the Vertex of a Triangle?
The altitude of a triangle is used to calculate the area of a triangle. Every triangle has three altitudes. Using the altitude of a triangle formula we can calculate the height of a triangle.
The altitude of a Triangle Formula can be expressed as:
\[\text{Altitude}= \frac{(2 \times \text{Area})}{\text{Base}}\]
where,
The area is the area of a triangle and the base is the base of a triangle
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According to different measures of different triangles, there are different types of altitudes of a triangle:
The altitude of an Obtuse triangle
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The altitude of the Equilateral Triangle
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The altitude of a Right Triangle formed by altitude on hypotenuse
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What is Signified by the Vertex of a Triangle?
The vertex or the vertices are the corners of a particular triangle. Since a triangle has three corners, that is why the vertices earthquake in numbers. The vertices of a triangle refer to the perpendicular line that can be drawn from the base or the middle point of the base to the opposite corner of the triangle. In the case of equilateral triangles, the length of all the sides is equal.
That is why, in case of equilateral triangles, the line segment that is perpendicular from the middle point of the base of the triangle to the opposite vertex can be drawn from anywhere. But in case of an isosceles triangle, the line segment must be drawn from the base of the triangle to the opposite corner and in this case, the base will be the side of the triangle that is not equal in length to the other sides of the triangle.
How is the Concept of Elevation and Altitude Comparable?
The concept of elevation is included in the subject of geography and it refers to the height of a particular place from the sea level. Altitude can sometimes mean the same and generally refers to the distance or height of a particular place from the earth's surface. The concept of altitude can be introduced in geography, physics and mathematics as well and it can denote different things depending on the subject.
How to Solve the Equations and Understand the Concept of Altitude?
Understanding a particular concept demands the full concentration of the students. To understand the concept of altitude, the students must get familiarized with the different kinds of triangles. Since the idea of altitude depends on the type of triangle and the length of the three sides of the triangle, it is better for the students if they can understand the concept of different types of triangles.
They can refer to other text books and reference books as well to get a detailed understanding of the topic. They can also refer to the books of other subjects to get an idea how the concept is associated. They can also try to analyze the concepts in their minds to understand the properties of altitude.
Since this concept is very important and they may expect questions related to the chapter on altitude, they can try solving the mock papers and question papers and get familiarized with the pattern of questions they may need to deal with, in the examinations. The most important thing that they should remember is to learn time management skills. If they are asked to elaborate the concept of altitude in the examinations, they need to draw proper diagrams and also write the concept in the proper language. The diagrams will make the process of understanding the concept easier for them. In the end, they should also get detailed information of the various types of altitude like the density, true, absolute altitude etc.
FAQs on Altitude of a Triangle
1. What is the Difference Between Altitude and Median?
Altitude and the median are two different things.
Altitude is a line segment drawn from the vertex to the opposite side of a triangle such that it is perpendicular to it, whereas the median is just a line drawn from the vertex of a triangle to the midpoint of the opposite side of the triangle.
A median need not be perpendicular to the side of the triangle. While an altitude need not touch the midpoint.
The intersection of the median is a centroid, while altitudes intersect at the orthocenter.
But in the case of some triangles like an equilateral triangle, the median and altitude are the same.
From the below figure it is clear that altitude and median are two different things.
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2. What makes an Isosceles Triangle?
A triangle whose two sides are equal is said to be an isosceles triangle. The base angles of an equilateral triangle are equal to each other. The two equal sides of an isosceles triangle are called ‘legs’ whereas the third unequal side is known as the ‘base’.
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The above figure is an example of an isosceles triangle, where the equal sides are of length ‘b’ and the unequal side has length ‘a’. And h is the height(altitude) of a triangle.
The altitude of the isosceles triangle can be calculated by the formula
\[h =\frac{\sqrt{(a^{2}-b^{2}}}{4})\]
3. What is an Example of Altitude?
The distance above the sea level, is a real-life example of altitude. The highest altitude point on the earth is Mount Everest. High-altitude zones are always much colder than the areas near the sea level. This is because the area with high altitudes has decreased air pressure. The human body reacts to this because less oxygen is available for breathing. People living in high altitudes often have a high risk of altitude sickness. It may have serious consequences as brain or lung damage.
4. How are the median and altitude of a triangle comparable?
There is a basic difference between the concept of median and altitude of a triangle. Median signifies a particular line segment that can join the vertex of a particular triangle and the middle point of the opposite side of the triangle. The altitude of a triangle refers to the line segment that can join the vertex of a triangle and the opposite side of the triangle in a way so that the line segment can be perpendicular to the opposite side of the triangle.
5. What is the importance of learning the concept of the altitude of a triangle?
The concept of altitude of a triangle is not only important for the students of physics, but also it becomes equally helpful for those who are students of geography. The altitude of a triangle is included in the syllabus of geometry and it helps students to understand various measurements and the concepts related to them. It also helps them to understand why a particular triangle is equilateral.
The students who want to pursue their career in the field of engineering and physics or mathematics, need to understand the concept of altitude so that they can be perfect at measuring something. The students who plan to undertake research projects in the field of geography should learn the concept of altitude because it helps them to measure the distance of a particular place from the sea level.
In case the students are having any difficulty understanding the concept of altitude, they can refer to the various articles published on the website of Vedantu and to the various NCERT books and solutions that can help them to get a detailed overview of the particular topic. They can also join and register for the free classes to directly communicate with the mentors and all their doubts related to this topic.