Answer:
Length of the pole is 27ft. ( rouding up to the nearest foot)
Explanation:
To solve this problem you need to understand that the the shadow cast by the pole on the ground connected to the pole itself and to the imaginary line of sun light forms a triangle with 3 different angles, please see the drawing to a better understanding.
* The sum of the internal angles of any triangle must be 180° then;
α: angle of the elevation of the sun= 64°
angle of the pole to the ground= (90-19)= 71°
β = 180 - ( 64+71) = 45°
*To find the length of the pole we can use the law of Sines;
|BC| / sin (α) = |AC| / sin (β)
|BC|= Length of the pole
|AC|= shadow of the pole on the ground which is known to be 21 ft
|BC| / sin (64°) = 21 / sin (45°)
|BC|= 21 x [sin (64°)/ sin (45°)]
|BC|= 21 x 1.27≅ 26.67 ft
To find the temperature it is necessary to use the expression and concepts related to the ideal gas law.
Mathematically it can be defined as
Where
P = Pressure
V = Volume
n = Number of moles
R = Gas constant
T = Temperature
When the number of moles and volume is constant then the expression can be written as
Or in practical terms for this exercise depending on the final temperature:
Our values are given as
Replacing
Therefore the final temperature of the gas is 800K