Question

I really need help with this, thank you!!!

Answer 1

6. 60°; 7. 5.20; 8. 7.96

Explanation:

5. Draw ∆ABC

See Fig. 1 below

6 . Determine m∠C

∠A + ∠B + ∠C = 180

40 + 80 + ∠C = 180

120 + ∠C = 180 Subtract 120 from each side

m∠C = 60°

7. Determine a.

By the law of sines,

a/sinA = c/sinC Multiply each side by sin A

a = c(sinA/sinC)

= 7 × (sin40/sin60)

= 7 × 0.6428/0.8660

= 5.20

8. Determine b.

b/sinB = c/sinC Multiply each side by sin B

b = c(sinB/sinC)

= 7 × (sin80/sin60)

= 7 × 0.9848/0.8660

= 7.96

Answer 2

6. 60°

7. 5.19559

8. 7.96011

Explanation:

6. The sum of angles in a triangle is 180°, so the remaining angle is ...

180° -40° -80° = 60°

7. The lengths of sides are proportional to the sine of the opposite angle (Law of Sines).

a = c·sin(A)/sin(C) = 7·sin(40°)/sin(60°) ≈ 5.19559

8. Same explanation as 7.

b = c·sin(B)/sin(C) = 7·sin(80°)/sin(60°) ≈ 7.96011