Mary Beth has taught 1st, 4th and 5th grade and has a specialist degree in Educational Leadership. She is currently an assistant principal.
Let's Build a Treehouse!
Let's pretend that you are building a treehouse! You rest a ladder against the top of the tree trunk, but it is too tall for you to climb (safety first, kids). Is there any way that you could measure the height of the tree trunk? Yes there is! If you know the angle of the slant of the ladder and how far the ladder is from the tree, then all you need in order to figure out the height of the tree trunk is trigonometry.
What is Trigonometry?
Trigonometry is a blend of calculation and geometry. When studying trigonometry, you are looking at the relationship between the angles and sides of triangles. Did you notice the 'tri' in triangle and trigonometry? Don't get it twisted. Trigonometry isn't only about triangles! Many shapes can be broken into multiple triangles, so your knowledge of trigonometry can help you with many other shapes. Trigonometry uses formulas to help you figure out unknown measurements of the sides and angles of triangles.
History of Trigonometry
Did you know that trigonometry actually started out as a way to study planets and stars? A long time ago, people thought that the planets and stars revolved around the Earth. Of course, we know the exact opposite is true. Stars have a fixed position in the sky and the Earth and other planets revolve around the Sun. In order to study this movement, an astronomer named Hipparchus realized that you could connect the Earth with other planets or stars with imaginary right triangles (triangles with an angle shaped like a corner). And, trigonometry was born! Hipparchus is known as the Father of Trigonometry.
The most important things to know in trigonometry are three main functions, which are kind of like secret codes. Before you get the secret codes, you have to know the special names for the sides of a right triangle.
- Hypotenuse: The longest side of the triangle; it is always 'across the street' from the right angle
- Adjacent: The side next to the angle that you are trying to measure - think of it being the 'next door neighbor' of the given angle
- Opposite: The side across from the angle that you are trying to measure - think of it being 'across the street' from the given angle
Now that know the special names of the sides, you are ready to learn the ratios.
- Sine = Opposite/Hypotenuse
- Cosine = Adjacent/Hypotenuse
- Tangent: Opposite/Adjacent
When you learn trigonometry, you will learn how to use these ratios to find the missing length of a triangle's side.
Trigonometry in the Real World
Sometimes, we learn things in school and wonder how we will ever use this in the real world. While trigonometry might seem like something that you will only do in school, there are actually many real-world situations when you will need to understand trigonometry. For example, there are many jobs that involve trigonometry like engineers, scientists, architects and astronomers. Trigonometry is also used in other math and science classes that you will take later in life, like physics and calculus.
Trigonometry is the study of the relationships between sides and angles of triangles. You will need to know many vocabulary words to understand trigonometry, such as hypotenuse which is the longest side of a right triangle or adjacent which is the side that is next to the given angle.
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