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