Special Right Triangles: 30-60-90 and 45-45-90
This page focuses on two special types of right triangles: the 30-60-90 triangle and the 45-45-90 triangle. These triangles have unique properties and ratios that make them particularly useful in geometry and trigonometry.
The 30-60-90 triangle is described as half of an equilateral triangle. Its side ratios are 1 : √3 : 2, corresponding to the shortest side (opposite to 30°), the side opposite to 60°, and the hypotenuse, respectively.
Definition: A trójkąt 30 60 90 is a right triangle with angles of 30°, 60°, and 90°, formed by bisecting an equilateral triangle.
The 45-45-90 triangle is presented as half of a square. Its two legs are equal, and the hypotenuse is √2 times the length of a leg.
Highlight: The side ratios in a 45-45-90 triangle are 1 : 1 : √2, representing the two equal legs and the hypotenuse.
An example problem is provided, involving a square-shaped plaza with an underground cable running along its diagonal. The problem demonstrates how to use the properties of a 45-45-90 triangle to calculate the area of the square given the length of its diagonal.
Example: Given a diagonal (cable length) of 10m, the side length of the square is calculated as 5√2 m, resulting in an area of 100 m².
The page also touches on the concept of zależności w trójkącie 30 60 90 (relationships in a 30-60-90 triangle) and zależności w trójkącie 45 45 90 (relationships in a 45-45-90 triangle), which are crucial for solving various geometric problems.
