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angle of a right triangle can be known if the lengths of the three sides of the triangle are
known. In many cases, it is often asked to specify the value of a function. If the angle

measure is given. For special angles 30°, 45°, and 60° , we can use geometry to determine
the value.

A right triangle with an angle of 45° actually has two angles of 45° . So the right triangle

is isosceles and the lengths of the sides are the same. For example, take the length of the
right side as 1. Then we can determine the length of the hypotenuse using the

Pythagorean theorem as follows.

The right triangle above is shown in the image below. Based on the figure, we can easily

determine the value of a trigonometric function from an angle of 45°.

To determine the value of the other three functions, all you have to do is find the

reciprocal values of sin, cos, and tan. We can also determine the value of the function of
the angles 30° and 60° . A right triangle with angles 30° and 60° is half of an equilateral

triangle as shown in the following figure. If the length of the sides of an equilateral
triangle is 2, then we have a right triangle with the length of the hypotenuse 2 and the

length of one of the sides being 1. The length of the other side, , can be determined using

the Pythagorean theorem.