The side of the PQR is the exterior angle of the triangle extending the QR on both sides Get PQs and PRT. If POS = 1000 and If PRT = 1300, find the size of each corner of the PQR
Answers
A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted {\displaystyle \triangle ABC}\triangle ABC.[1] In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane (i.e. a two-dimensional Euclidean space). In other words, there is only one plane that contains that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is only one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is no longer true. This article is about triangles in Euclidean geometry, and in particular, the Euclidean plane, except where otherwise noted.
There are a few methods of obtaining right triangle side lengths. Depending on what is given, you can use different relationships or laws to find the missing side:
Given two sides
If you know two other sides of the right triangle, it's the easiest option; all you need to do is apply the Pythagorean theorem:
a² + b² = c²
if leg a is the missing side, then transform the equation to the form when a is on one side, and take a square root:
a = √(c² - b²)
if leg b is unknown, then
b = √(c² - a²)
for hypotenuse c missing, the formula is
c = √(a² + b²)
Given angle and hypotenuse
Right triangle with law of sines formulas. a over sin(α) equals b over sin(β) equals c, because sin(90°) = 1
Apply the law of sines or trigonometry to find the right triangle side lengths:
a = c * sin(α) or a = c * cos(β)
b = c * sin(β) or b = c * cos(α)
Given angle and one leg
Find the missing leg using trigonometric functions:
a = b * tan(α)
b = a * tan(β)
Given area and one leg
As we remember from basic triangle area formula, we can calculate the area by multiplying triangle height and base and dividing the result by two. A right triangle is a special case of a scalene triangle, in which one leg is the height when the second leg is the base, so the equation gets simplified to:
area = a * b / 2
For example, if we know only the right triangle area and the length of the leg a, we can derive the equation for other sides:
b = 2 * area / a
c = √(a² + (2 * area / a)²)