how to solve this

[lone vigil]

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[neon robin]

What two segments?

DF = 12.

Are you referring to DC and AD?

[fossil jasper]

It says find the x

Pf?

[neon robin]

Soln: ||Maybe we can say sin of ADB = 6/12 = 1/2 and hence prove its 30 degrees.

Like that DFA = 60.

DAF = 90.

Just like that EPF = 90.

PEF = DFA = 60.

cos(60) = adj/hyp = x/4.
cos(60) = 1/2 which implies x =8.||

This is how I got it but it could be wrong.

Don't trust it blindly.

[fossil jasper]

alright thanks man

[slender ocean]

Hmm

I got a different answer for x

[neon robin]

What?

[subtle shuttle]

Couldn't find an attached image in the last 10 messages.

Apr 10, 2024, 4:50 PM

[slender ocean]

Can you elaborate on how you got EPF as 90 degrees?

because sin(ECB) = 1/2

so angle CEB should be 60 degrees

therefore angle PEA is 180-60 = 120 degrees

Angle DPE is 180-90 = 90 degrees

Angle ADP is 30 degrees

and Angle DAE is 90 degrees

so quadrilateral DAEP = DPE + ADP + DAE + PEA

and that is 90 + 30 + 90 + 120 = 330 degrees

and the angles of a quadrilateral cannot add up to 330 degrees

I used similarity

Since DPC and EPF can be proven similar by AA similarity

we know EF is 4 and DC is 8 because of the properties of a parallelogram

so EF/DC = 4/8 = 1/2

so the sides are in a ratio of 1 to 2

we have DF = DP + PF

and we know DP = 2PF

Then we can solve from there since we know the value of DF

[fossil jasper]

+close