The problem refers to triangle abc. find the area of the triangle. round to three significant digits. b = 9° 20', c = 80° 40', b = 2.92 ft

Area of the triangle is 25.9 feet²

Step-by-step explanation:

* Lets explain how to solve the problem

- In Δ ABC

∵ m∠ B = 9° 20' = 9 + 20/60 = (28/3)°

∵ b = 2.92 feet

- b is the side opposite to angle B

∵ m∠ C = 80° 40' = 80 + 40/60 = (242/3)°

- Lets find c the side opposite to angle C by sing the sine rule

∵

∴

- By using cross multiplication

∴

- The area of the triangle = 1/2 (b)(c)sin∠A

∵ The sum of the interior angles of a triangle is 180°

∴ m∠ A + m∠ B + m∠ C = 180°

∵ m∠ B = (28/3)°

∵ m∠ C = (242/3)°

∴ m∠ A + 28/3 + 242/3 = 180

∴ m∠ A + 90° = 180° ⇒ subtract 90 from both sides

∴ m∠ A = 90°

∴ Area of the triangle = 1/2 (2.92)(17.77) sin(90)

∵ sin(90) = 1

∴ Area of the triangle = 1/2 (2.92)(17.77) = 25.9 feet²

* Area of the triangle is 25.9 feet²

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a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional