Applications of Trigonometry
Right-angled Triangle or Right Triangle

Solving right triangles
Solving right triangles examples
Right-angled Triangle or Right Triangle
Trigonometric functions of an acute angle defined in a right triangle
Trigonometric functions of an acute angle are defined in a right triangle as a ratio of its sides.
Solving the right triangle
To solve a right triangle means to find all unknown sides and angles using its known parts.
While solving a right triangle we use Pythagoras’ theorem and trigonometric functions of an acute angle depending which pair of its parts is given.
Note, right triangles are usually denoted as follows;  c stands for the hypotenuse,  a and b for the perpendicular sides called legs, and a and b for the angles opposite to a and b respectively.
There are four basic cases that can occur, given
a) hypotenuse and angle,            c) hypotenuse and leg,
b) leg and angle,                         d) two legs.
Solving right triangles examples
Example:   Which highest level h will reach a bob pendulum of length l, starting from rest, where j is the largest angle attained by the pendulum.
Solution:  Given l and j.    h = ?
 From the right triangle in the right figure

Example:   In an isosceles triangle two equal sides subtend angles a at the endpoints of the third side.
What is the length of the third side if the difference between the altitude of the triangle to that side, and the radius of the inscribed circle, equals d?
Solution:  Given a and d.    a = ?
 angle ESC = angle EAD = a  - the angles with mutually perpendicular sides

Example:   Given is the sum a + b of legs and the angle a of a right triangle. Find its hypotenuse c and the sides, a and b, see the figure below.
Solution:  Given a + b and a.    a, b and c = ?