Trigonometric ratios
Because a triangle has three sides, you can set six reasons, two between each pair of these sides. Trigonometric ratios of an acute angle in a right triangle are: Breast
: ratio between the leg opposite the angle and the hypotenuse.
Cosine: ratio between the leg adjacent to angle and the hypotenuse.
Tangent: ratio between the leg opposite the angle and the adjacent leg.
Cotangent: ratio between the leg adjacent to angle and the opposite leg. Drying
: ratio between the hypotenuse and the side adjacent to angle.
Cosecant: ratio between the hypotenuse and the leg opposite the angle.
Pythagorean Theorem:
"In any triangle, the square of the hypotenuse equals the sum of the squares of the legs." And, "In any triangle, the square of one of the legs is equal to the difference between the square of the hypotenuse and the square of the other leg." Exercises
resolved
S olutions
1. To calculate the six trigonometric ratios as we need to find the other leg, that we do apply the Pythagorean Theorem . Having found the value of this leg, we proceed to find the values \u200b\u200bof reason by their respective definitions :
2. First find the value of the hypotenuse using the Pythagorean Theorem , then calculate the trigonometric ratios, from their definitions and dice the data obtained:
triangles Resolution
Solving a triangle means finding the numerical value of each of its three sides and three angles. In this kind of problems always give us the values \u200b\u200bof three elements, one of which is one of the sides, and asked to find the other three. Elementary plane geometry we know that "the sum of the measures of the three interior angles in any triangle is 180 degrees." Thus, to find the value of the third angle, knowing the other two, simply use the following formula:
With the little we have studied so far, we are able to solve right triangles when given the value of one corner and that of one side. However
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