Right triangle trigonometry: medium

In triangle

A B C

, the measure of

∠ A

90^{\circ}

A B = 10

, and

B C = 16

. Triangle

D E F

is similar to triangle

A B C

, where vertices

D

E

, and

F

correspond to vertices

A

B

, and

C

, respectively, and each side of triangle

D E F

2

times the length of the corresponding side of triangle

A B C

. What is the value of

\sin F

How do I enter a student-produced response on the SAT?

For student-produced response questions, solve each problem and enter your answer as described below.

If you find more than one correct answer, enter only one answer.
You can enter up to 5 characters for a positive answer and up to 6 characters (including the negative sign) for a negative answer.
If your answer is a fraction that doesn’t fit in the provided space, enter the decimal equivalent.
If your answer is a decimal that doesn’t fit in the provided space, enter it by truncating or rounding at the fourth digit.
If your answer is a mixed number (such as $3 \frac{1}{2}$ ‍), enter it as an improper fraction ( $\frac{7}{2}$ ‍) or its decimal equivalent ( $3.5$ ‍).
Don’t enter symbols such as a percent sign, comma, or dollar sign.

Examples:

Answer	Acceptable ways to enter answer	Unacceptable: will NOT receive credit
$3.5$ ‍	$3.5$ ‍ , $3.50$ ‍ , $\frac{7}{2}$ ‍	$\frac{31}{2}$ ‍ , $3$ ‍ $\frac{1}{2}$ ‍
$\frac{2}{3}$ ‍	$\frac{2}{3}$ ‍ , $.6666$ ‍ , $.6667$ ‍ , $0.666$ ‍ , $0.667$ ‍	$0.66$ ‍ , $.66$ ‍ , $0.67$ ‍ , $.67$ ‍
$- \frac{1}{3}$ ‍	$- \frac{1}{3}$ ‍ , $- .3333$ ‍ , $- 0.333$ ‍	$- .33$ ‍ , $- 0.33$ ‍

Digital SAT Math