In ΔABC, c = 4.2 inches, ∠C=24° and ∠A=115°. Find the area of ΔABC, to the nearest 10th of an square inch.

12.9

Step-by-step explanation:

So to find the area of this triangle, you will need to use the equation

Area = c*b*sin(A) = a*b*sin(C)

Here, we have ∠A, ∠C, and side c

We can use the fact that so solve for the other variables we do not have.

First we can find the other angle B. Since ∠A + ∠B + ∠C = 180°,

∠B = 180° - ∠A - ∠C, which is ∠B = 180° - 115° - 24° = 41°

Now that we have all three angles, we can solve for the sides

Since we only have side c, we will manipulate the equation with c and one of the others to solve for a or b. Let's solve for side b first.

Since , solving for b would give us . Then plugging in our values we get = 6.77 = b

Now we can solve for the remaining side, a, using the same method.

Since , solving for a would give us . Then plugging on our values we get = 9.36 = a

Now that we have all our angles and sides, we can plug in our numbers to either of our area equations ⇒

Area =c*b*sin(A)= (4.2)(6.77)sin(115) = 12.9 or a*b*sin(C) = (9.36)(6.77)sin(24) = 12.9

answer

step-by-step explanation:

answer: the answer is b. i think hope i got it correct

step-by-step explanation: