Answer:
12.8
Step-by-step explanation:
Given a parabola in standard form , ax² + bx + c : a ≠ 0
Then the x- coordinate of the vertex is
= -
h = 3 + 14t - 5t² ← is in standard form
with a = - 5 and b = 14, thus
= -
= 1.4
Substitute t = 1.4 into h for maximum height
h = 3 + 14(1.4) - 5(1.4)²
= 3 + 19.6 - 9.8 = 12.8
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
