Chapter 7 Right Triangles and Trigonometry Flashcards
ambiguous case
given the measures of two sides and a nonincluded angle, there exist two possible triangles using the Law of Sines
angle of depression
the angle between the line of sight and the horizontal when an observer looks downward
angle of elevation
the angle between the line of sight and the horizontal when an observer look upward
cosine
for an acute angle of a right triangle, the ratio fo the measure of the leg adjacent to the acute angle to the measure of the hypotenuse
geometric mean
for any positive numbers a and b, the positive number x such that a/x=x/b
Law of Cosines
used to solve for a missing side or angle of a triangle when you know two sides and an included angle
Law of Sines
used to solve for a missing side or angle of a triangle when you know two sides and a nonincluded angle or one side and two angles.
Pythagorean identity
the identity cos^2(x)+sin^2(x)=1
Pythagorean triple
a group of three whole numbers that satisfies the equation a^2+b^2=c^2, where c is the greatest number
reciprocal identities
Each of the three trigonometric ratios called cosecant, secant, and cotangent, that are the reciprocals of sine, cosine and tangent, respectively.
sine
for an acute angle of a right triangle, the ratio of the measure of the leg opposite the acute angle to the measure of the hypotenuse
solving a triangle
finding the measure of all of the angles and sides of a triangle
tangent
for an acute angle of a right triangle, the ratio of the measure of the leg opposite the acute angle to the measure of the leg adjacent to the acute angle.
trigonometric identity
an equation involving a trigonometric ration that is true for all values of the angle measure
trigonometric ratio
a ratio of lengths of sides of a right triangle
