Answer:
Answers are in bold
Explanation:
Question 1
For a 30-60-90 triangle:
Longer leg: sqrt(3) * (shorter leg) -> AC=BC*sqrt(3)
Hypotenuse: 2 * (shorter leg) -> AB=2*BC
It is given that AC, the longer leg, is 18, therefore we can each side length:
Shorter Leg:
18=BC*sqrt(3)
10.39230485=BC
BC=10.39230485
BC=6sqrt(3) <-- Simplified Form
Hypotenuse:
AB=2*10.39230485
AB=20.78460969
AB=12sqrt(3) <-- Simplified Form
Question 2
The sequence is geometric because each consecutive term is being multiplied by 2. Therefore, the common ratio is r=2.
Question 3
You got this one right, so no need to talk about it