Question

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In triangle ABC, the measure of ∠B is 90°, BC=16, and AC=20. Triangle DEF is similar to triangle ABC, where vertices D, E, and F correspond to vertices A, B, and C, respectively, and each side of triangle DEF is
$\frac{1}{3}$
the length of the corresponding side of triangle ABC. What is the value of sin F?


only those will answer who know it ​

Answer 1

• AC is hypotenuse of triangle of ABC
• AB and BC are legs of right angle triangle of ABC

Using Pythagorean theorem -

AB = √20² - 16²

AB = √400 - 256

AB = √144

AB = 12

• Since DEF is similar to the triangle ABC with vertex F corresponding to vertex C

• Angel F = Angle C

Therefore,

$\sin(F) = \sin(C)$

Now,

From Length of triangle ABC,

$\sin(F) = \frac{opposite \: side}{hypotenuse}$

$\frac{AB}{AC} = \frac{12}{20} = \frac{3}{5}$

Therefore,

$\sin(F) = \frac{3}{5}$

or 0.6

Answer 2

Given :-

∠B= 90°

BC= 16 .

AC= 20 .

_______

To Find AB we have to apply Pythagoras theorem :

$AB = \sqrt{ {20}^{2} - {16}^{2} }$

$= \sqrt{144}$

$AB = 12.$

☆ now DEF is exactly similar to ABC But all the sides are 1/3 to the side of ABC.

So;

$DF = \frac{20}{3}$

$EF = \frac{16}{3}$

$Sin F = \frac{P}{H}$

$= \frac{DE}{DF}$

$= \frac{ \frac{12}{3} }{ \frac{20}{ 3} }$

$= \frac{12}{20}$

$= \frac{3}{5}$

or

${\pink{\tt{0.6}}}$

$\sf\red{hope\:it\:helps\:you}$