Right Triangle Trigonometry
Right Triangle Trigonometry
Right-triangle trigonometry has many applications. That is the ability to compute the lengths of sides of a triangle makes it possible to find the height of a tall object.
Right Triangle
A right-angle has a value of 90 degrees (90∘). It is a triangle in which one angle is a right angle. The relation between the angles and sides of a right triangle is the basis for trigonometry.
The hypotenuse is the side opposite the right angle (side c). And the legs are sides adjacent to the right angle (sides a and b). Side a may be identified as the side adjacent to angle B and opposed to (or opposite) angle A And side b is the side adjacent to angle A and opposed to angle B.
There are several ways to determine the right triangle. One of these ways is the Pythagorean Theorem, which states that.
Suppose you have a right triangle in which a and b are the lengths of the legs, and c is the length of the hypotenuse,
Understanding Right Triangle Relationships
Given a right triangle having acute angle of t
sin(t) = Opposite/Hypotenuse
cos(t) = Adjacent/Hypotenuse
tan(t) = Opposite/Adjacent
Special Angles
As a general rule, to use a calculator to find the values of the trigonometric functions for any particular angle measure And angles that measure 30°, 45°, and 60° which you will see in many problems and applications are special.
A right triangle has an acute angle that measured 45°. So the acute angles are complementary, the other one must also measure 45°, because the two acute angles are equal, the legs must have the same length
for example, 1 unit.
You can determine the hypotenuse using the Pythagorean Theorem.
12+12=h2
1+1=h2
2=h2
h2=2
Now all the sides and angles are in this right triangle.
You can use this triangle (which is sometimes called a 45° – 45° – 90° triangle) to find all of the trigonometric functions for 45°. One way to remember this triangle is to note that the hypotenuse is times the length of either leg.
Also, read Measuring in space