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How to find an angle in a right triangle


How to find an angle in a right triangle</a>

Already from the very name of the "rectangular" triangle it becomes clear that one corner in it is 90 degrees.

The remaining angles can be found by recalling simple theorems and properties of triangles.

You will need

  • Table of sines and cosines, Bradys table



Denote the angles of the triangle by the letters A, B and C, asThis is shown in the figure. The angle of the BAC is 90º-, the other two angles are denoted by the letters α- and β-. The triangle's triangle's letters are designated by the letters a and b, and the hypotenuse by the letter c.

In this figure, all the notation that will be used in the article


Then sinα- = b / c, and cosα- = a / c.

Similarly, for the second acute angle of the triangle: sinβ- = a / c, and cosβ- = b / c.

Depending on which sides we know, calculate the sines or cosines of the angles and look at the Bradys table for α- and β-.


Having found one of the angles, we can recall that the sum of the interior angles of a triangle is 180º-. Hence, the sum of α- and β- is equal to 180º- - 90º- = 90º-.

Then, calculating the value for α- from the tables, we can use the following formula to find β-: β- = 90º- - α-


If one of the sides of the triangle is unknown, thenWe apply the Pythagoras theorem: a²- + b²- = c²-. We derive from it the expression for the unknown side through the other two and substitute it in the formula to find the sine or cosine of one of the angles.

How to find an angle in a right triangle Was last modified: June 21st, 2017 By Fyyxoahr
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