Can someone help me solve for which expression?

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Answer 1 · 2018-06-08T20:49:59

The base of the triangle is side $b = e$ ,

Please observe that all of the selections use the angle $D$ ; the correct equation for the height using the sine of angle $D$ is:

$h = f sin(D)$

Substituting into the $A = 1/2bh$ formula:

$A = 1/2e f sin(D)$

This is the fourth selection.

Answer 2 · 2018-06-08T20:52:41

4th option

$sin D=h/f$ so $h=fsinD$

$A=1/2xxbasexxheight$

$A=1/2xxexxfsinD$

$A=1/2efsinD$

Answer 3 · 2018-06-08T21:02:22

$h=fsinD," " A=1/2 ef sin D$

Notice how all options involve $sinD$ .

Remember the definition of $sin D = "opposite"/"hypotenuse"$ for any right triangle in which $D < 90^@.$

In the small right triangle on the left, $h$ is the "opposite" side to $D$ and $f$ is the hypotenuse. Thus, we have:

$sin D = h/f$

We can solve this for $h$ by multiplying both sides by $f:$

$f sin D = cancelf * h/cancelf$

$=> color(red)h = color(red)(f sin D)$

We now have an expression for $h$ in terms of $f$ and $D.$

Using the classic formula for the area of a triangle $A= 1/2 bh,$ where

$b=e$ $" "$ (side $e$ is our base $b$ )

$h = f sin D$ $" "$ (from above)

we can now replace $h$ with its equivalent expression, as such:

$A = 1/2 ecolor(red)h$

becomes

$A = 1/2 ecolor(red)(fsinD)$