Answer:
55.04 ft²
Step-by-step explanation:
Calculate the area of the square, the area of the circle, then subtract the area of the circle from the area of the square.
Area of square = 16 x 16 = 256 ft²
Area of circle = r²
radius = 16 ÷ 2 = 8
⇒ Area of circle = 3.14 x 8² = 200.96 ft²
Shaded area = 256 - 200.96 = 55.04 ft²
Answer:
The measure of angle B is 41.5°
The length of side a is 30.6 feet ⇒ to the nearest tenth
The length of side b is 32.9 feet ⇒ to the nearest tenth
Step-by-step explanation:
In the given Δ ABC
∵ m∠A = 38.1°
∵ m∠C = 100.4°
→ By using the fact above
∵ m∠A + m∠B + m∠C = 180°
∴ 38.1 + m∠B + 100.4 = 180
→ Add the like terms in the left side
∴ 138.5 + m∠B = 180
→ Subtract 138.5 from both sides
∴ m∠B = 41.5°
∴ The measure of angle B is 41.5°
∵ a is the opposite side of ∠A
∵ b is the opposite side of ∠B
∵ c is the opposite side of ∠C
→ By using the sine rule
∴ =
=
∵ c = 48.4 ft, m∠A = 38.1°, m∠B = 41.5°, and m∠C = 100.4
→ Substitute them in the sine rule above
∴ =
=
→ By using cross multiplication between the 1st and the 3rd fractions
∴ a × sin 100.4 = 48.8 × sin 38.1
→ Divide both sides by sin 100.4
∴ a = 30.61429861
∴ The length of side a is 30.6 feet ⇒ to the nearest tenth
→ By using cross multiplication between the 2nd and the 3rd fractions
∴ b × sin 100.4 = 48.8 × sin 41.5
→ Divide both sides by sin 100.4
∴ b = 32.87596206
∴ The length of side b is 32.9 feet ⇒ to the nearest tenth