Big ideas math geometry- Chapter 9 vocab
If cos D = sin F, create an expression for D in terms of F.
D = 90 - F
Pythagorean Inequalities Theorem
If a²+b²>c², the triangle is acute. If a²+b²<c², the triangle is obtuse.
Converse of the Pythagorean Theorem
If the square of the length of the longest side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.
Pythagorean Theorem
In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs
tangent ratio (tan)
Length of leg opposite/ length of leg adjacent; a trigonometric ratio for acute angles that involves the lengths of the legs of a right triangle
angle of depression
The angle formed by a horizontal line and the line of sight to an object below the horizontal line
sine and cosine of complementary angles
The sine of an acute angle is equal to the cosine of its complement. The cosine of an acute angle is equal to the sine of its complement. sin A = cos(90˚- A) = cos B
Pythagorean triple
a set of three whole numbers that satisfy the Pythagorean Theorem
inverse tangent
an inverse trigonometric ratio, abbreviated as tan-1; use this to solve for a missing angle
sin 23 degrees = cos _________________ ?
cos 67 degrees
<A and <B are acute angles in triangle ABC. If sin A = 8/17, what is cos B?
cos B = 8/17
cosine ratio (cos)
length of leg adjacent/ length of hypotenuse
sine ratio (sin)
length of opposite angle/ length of hypotenuse
cos 52 degrees = sin _______________ ?
sin 38 degrees
angle of elevation
the angle formed by a horizontal line and the line of sight to an object above the horizontal line
to solve a right triangle
to find the measures of all of the sides and angles of a right triangle. You can solve when you know the following: two side lengths, or one side length and the measure of one acute angle
sine and cosine
trigonometric ratios involving the lengths of a leg and hypotenuse of a right triangle
tan X = 3/4. What is the measure of <X?
36.87 degrees
sin B = 12/14. What is the measure of <B?
58.99 degrees
cos A = 5/13. What is the measure of <A?
67.38 degrees
inverse sine
An inverse trigonometric ratio abbreviated as sin-1; use this to solve for a missing angle
inverse cosine
An inverse trigonometric ratio, abbreviated as cosˉ¹; use this to solve for a missing angle