In triangle CDE, angle C measures 50°, angle D measures 70°, and side CE measures 10 m. Find the lengths of sides CD and DE.

The given values are

C = 50°, D = 70° and CE = 10 m

First, find angle E using the fact that the sum of angles in a triangle is 180°:

E = 180 - (C + D)

E = 180 - (50 + 70)

E = 60°

Now, let’s use the Law of Sines to find the length of side CD:

\$("CD")/("sinC") = ("DE")/("sinD") = ("CE")/("sinE")\$

Plug the value in the formula and then simplify for the value of CD

\$("CD")/("sin"(50)) = 10/("sin"(60))\$

\$"CD" = (10 times "sin"(50)) / ("sin"(60))\$

CD = 8.84 m

Now, let’s use the Law of Cosines to find the length of side DE:

\$"cosD" = (("CD")^2 + ("CE")^2 - ("DE")^2)/(2. "CD". "CE")\$

Rewrite the formula and then plug the value in the formula

\$("DE")^2 = ("CD")^2 + ("CE")^2 - 2 times "CD" times "CD" times "cos"("D")\$

\$("DE")^2 = (8.84)^2 + (10)^2 - 2 times 8.84 times 10 times "cos"(70)\$

simplify for the value of DE

\$("DE")^2 = 78.14 + 100 - 176.4 times 0.342\$

\$("DE")^2 = 117.674\$

\$"DE" = \sqrt(117.674)\$

DE = 10.84 m

So, the length of side CD is 8.84 m and side DE is 10.84 m.

Wrong: It suggests CD = 8.48 m and DE =10.84 m, which doesn’t match the calculations

CD = 8.48 m and DE = 10.84 m

Option B is incorrect because it doesn’t match the calculated values for both sides

CD = 8.48 m and DE = 10.48 m

Option C is correct because it matches these calculated values for CD and DE by using the law of sines and cosines formula

CD = 8.84 m and DE = 10.84 m

Incorrect: It suggests that DE = 10.48m, which is not the correct value based on our calculations

CD = 8.84 m and DE = 10.48 m

Option

C

Can you summarize what you’ve understood in the above steps?