Question

Yo yo yo check it peeps! I'd really appreciate any help I could get!!!

Given expression for the height h of △DEF, and use the expression to write a formula for the height of the triangle in terms of the variables shown by replacing h in the formula: A=1/2bh.

answer options and
picture file attached below

Answer 1

just a second for the file

Answer 2

a.) \[h=e sinD, A=1/2 e^2 sinD\]

b.)
\[h=d sinD, A=1/2ed sinD\]

c.)\[h=f sinD, A=1/2e (1/2f sinD)\]

d.) \[h=f sinD, A=1/2ef sinD\]

Answer 3

e on a segment? is that a variable or the constant e?

Answer 4

I'm not sure I am so sorry :(

Answer 5

nvm … replacing h
let me redo

Answer 6

k dokes no prob!

Answer 7

Okay so first of all the diagram really helps you, as it already hints at splitting the triangle into two right-angled triangles, which means we can use 'sohcahtoa' trig

Then using basic trigonometry, we can see that in the left hand side triangle, that we have
an angle 'D'
a hypotenuse 'f'
and we want to find 'h' which is opposite our angle 'D'

So as we have our angle, hypotenuse and want to find the 'opposite length'

We know that \[\sin D = opposite \div hypotenuse \]
So looking at your triangle we see that

Sin D = 'h' / f
So our length 'h' = f sin D

\[Area = \frac{ 1 }{ 2 } base * height\]

So the base is given, it is length 'e'
So
\[Area = \frac{ 1 }{ 2 } * e * f \sin D\]

Hope that helps :)

Answer 8

Hahahaha!! Well thanks guys!!

Answer 9

Definitely helps @sarahusher!

Answer 10

she's great isn't she?