Use the formula,

Area = (1/2)acsinB

= (1/2)(10)(7)sin80

= 35sin80

= 34.49 cm^2

you were right, your units were wrong!

Use the law of cosines:b) the length of CA

(CA)^2 = (AB)^2 + (BC)^2 - 2(AB)(BC)cosB

=> (CA)^2 = 10^2 + 7^2 - 2(10)(7)cos80

=> (CA)^2 = 149 - 24.31074487

=> (CA)^2 = 124.6892551

=> CA = sqrt(124.6892551)

=> CA = 11.17 cm

seems you were incorrect

what did you do to get your answer for this one?

Now that we know all the sides, we could use the cosine rule again, but for the sake of variety, let's use the sine rule a.k.a. the law of sinesc) the size of the angle C

Now b/sinB = c/sinC

=> AC/sinB = AB/sinC

=> sinC = AB/(AC/sinB)

=> C = arcsin[AB/(AC/sinB)]

=> C = arcsin[10/(11.17/0.984807753)]

=> C = arcsin(0.88165421)

=> C = 61.84 degrees