Math.Trig is a free iPhone app we have developed to help you calculate the angles and side lengths of triangles. If you need a bit of help with the math, then this page explaining the trigonometry formulas should help you.
Sum of The Angles
The sum of the internal angles of a triangle always add up to 180°. So if you know two angles of a triangle it’s simple to find the missing angle.
A + B + C = 180°
For example, if you know A = 20° and B = 80°
Then C = 180° - (20° + 80°) = 80°
Right triangles or right-angled triangles are a special type of triangle with one right angle, which is an angle of 90°. There are particular trigonometry rules and equations that can be used for right triangles.
The longest side of a right triangle is always opposite the right angle and is called the hypotenuse.
Pythagoras’ Theorem
Pythagoras’ Theorem is used to find the side lengths of a right triangle, it can be written like this: a² + b² =h²
For Example:
If you know the side lengths a = 3 and h = 5Then b² = h² - a²
⇒ b² = 25 - 9 =16
⇒ b = √16 = 4
So b has length 4
You can see a screenshot from Math.Trig of this triangle opposite.
There are three basic trigonometry rules associated with right triangles:sinϑ = opposite ÷ hypotenuse
cosϑ = adjacent ÷ hypotenuse
tanϑ = opposite ÷ adjacent
Sin, cos and tan are all trigonometry functions which can be applied to angles, in this case an unknown angle is called ϑ (theta). Hypotenuse refers to the length of the hypotenuse. Opposite means the side length opposite the angle used in the function and adjacent is the side adjacent (next) to this angle.
You can usually use more than one of these trigonometry equations to solve a right triangle.
For Example:
Using the right triangle in the previous example with side lengths: a = 3, b = 4 and h = 5. Find the angle A.Angle A is opposite side a and adjacent to side b, so you can use the trigonometry formula:
tanϑ = opposite ÷ adjacent
tanA = a ÷ b
⇒ tanA = ¾
You can use a scientific calculator to apply the inverse tan function:
A = arctan(¾) = 36.9° (1 decimal place)
Simple! Don't forget to check your answers with Math.Trig. You can see what this triangle looks like in the Math.Trig screenshot opposite.
