Question

Using the provided measures determine the length of the segment AC.

10.9cm


13.1cm


12.4cm


7.1cm

Answer 1

Answer: ~13cm

Step-by-step explanation: Since you didn't tell me which segments have those lengths, I'm gonna have to figure out myself

In a triangle, lengthier segments correspond to larger angles

m(ACB)=180-m(CAB)-m(ABC)=72 degrees

so m(ACB)=72>m(CAB)=70>m(CBA)=38

m(ACB) is opposite to AB

m(CAB) is opposite to BC

m(CBA) is opposite to AC

so AB>BC>AC

in the triangle DCA, with similar logic we find m(DCA)=90-m(CDA)=28 degrees

therefore m(CDA)=62>m(DCA)=22 so AC>DA

Now we know AB>BC>AC>DA

using the provided lengths we find:

AB=12.1 cm

BC=12.4 cm

AC=10.9 cm

DA=7.1  cm

with simple pythagoras theorem we obtain:

DC = sqrt(DA^2+AC^2) = sqrt(7.1*7.1+10.9*10.9) ~= 13 cm(approximately)