Can someone help me solve for which expression?

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3 Answers
Jun 8, 2018

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

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

h = f sin(D)h=fsin(D)

Substituting into the A = 1/2bhA=12bh formula:

A = 1/2e f sin(D)A=12efsin(D)

This is the fourth selection.

Jun 8, 2018

4th option

Explanation:

sin D=h/fsinD=hf so h=fsinDh=fsinD

A=1/2xxbasexxheightA=12×base×height

A=1/2xxexxfsinDA=12×e×fsinD

A=1/2efsinDA=12efsinD

Jun 8, 2018

h=fsinD," " A=1/2 ef sin Dh=fsinD, A=12efsinD

Explanation:

Notice how all options involve sinDsinD.

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

In the small right triangle on the left, hh is the "opposite" side to DD and ff is the hypotenuse. Thus, we have:

sin D = h/fsinD=hf

We can solve this for hh by multiplying both sides by f: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)