241 + 800 = 1041
247 + 794 = 1041
<u>Given</u>:
Given that ABC is a right triangle.
The length of AB is 7 units.
The measure of ∠A is 65°
We need to determine the length of AC
<u>Length of AC:</u>
The length of AC can be determined using the trigonometric ratio.
Thus, we have;

Where the value of
is 65° and the side adjacent to the angle is AC and the side hypotenuse to the angle is AB.
Substituting the values, we have;

Substituting AB = 7, we have;

Multiplying both sides by 7, we get;



Rounding off to the nearest hundredth, we get;

Thus, the length of AC is 2.96 units.
Answer: 
Step-by-step explanation:
Given
Position of the particle moving along the coordinate axis is given by

Speed of the particle is given by

Acceleration of the particle is

velocity can be negative, but speed cannot

So,
The length is always 1.5 times the width.
l = 1.5w
lw = 24
lw = 54
lw = 96
Or, we could put it this way:
1.5w(w) = 24
1.5w(w) = 54
1.5w(w) = 96
So,
1.5w^2=24
1.5w^2=54
1.5w^2=96
Dividing both sides by 1.5, we get:
w^2 = 16
w^2 = 36
w^2 = 64
And solving for the only logical dimension, we get:
w = 4
w = 6
w = 8
And their corresponding lengths:
l = 1.5(4) = 6
l = 1.5(6) = 9
l = 1.5(8) = 12
So a few lengths could be:
(l,w)
(6,4)
(9,6)
(12,8)
Of course, there are infinite solutions.