NY-G.SRT.6

GeometrySimilarity Right Triangles and Trigonometry60 target questions

Understand that by similarity side ratios in right triangles are properties of the angles in the triangle leading to definitions of trigonometric ratios for acute angles.

Sample Practice Questions (3)

In right triangle

A B C

, with the right angle at

C

, which ratio represents

sin (A)

\frac{opposite}{hypotenuse}

\frac{adjacent}{hypotenuse}

\frac{opposite}{adjacent}

\frac{hypotenuse}{opposite}

Triangle

A B C

is a right triangle with a right angle at

C

. Triangle

D E F

is similar to triangle

A B C

, with a right angle at

F

. If

m ∠ A = m ∠ D

, which statement must be true?

\frac{B C}{A B} = \frac{E F}{D E}

\frac{A C}{A B} = \frac{E F}{D E}

\frac{B C}{A C} = \frac{D F}{D E}

\frac{A B}{B C} = \frac{D E}{D F}

Triangle

A B C

and triangle

D E F

are similar right triangles where

∠ C

and

∠ F

are right angles. If the side lengths of

△ D E F

are twice the side lengths of

△ A B C

, which statement is true regarding the trigonometric ratios of

∠ A

and

∠ D

cos A = cos D

cos D = 2 \cdot cos A

sin A = 2 \cdot sin D

tan A = \frac{1}{2} tan D

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