Answer:
Using sine ratio:
[tex]\sin \theta = \frac{\text{Opposite side}}{\text{Hypotenusesside}}[/tex]
As per the statement:
The angle of elevation from Sara to kite in the sky is 53° and the length of the string is 32 feet. and Sara is 5 feet tall.
⇒Angle of elevation( [tex]\theta[/tex]) = 53° and
Hypotenuse side = 32 feet (As you can see the figure as shown below)
then;
Apply the sine ratio in triangle ACE we have;
[tex]\sin 53^{\circ} = \frac{CE}{32}[/tex]
[tex]0.79863551004 = \frac{CE}{32}[/tex]
Multiply both sides by 32 we get;
[tex]0.79863551004 \cdot 32 = CE[/tex]
Simplify:
CE = 25.5563363215 feet.
Then:
DE = CD+CE = 5 + 25.5563363215 = 30.5563363215 ≈30.6 feet.
Therefore, 30.6 feet far off the ground is the kite.
Answer: The answer is 30.56 feet.
Step-by-step explanation: As shown in the attached figure, Sara is flying a kite at the park with angle of elevation from Sara to kite in the sky, ∠BAC = 53° and length of the string, AC = 32 feet. Sara is 5 feet tall. We need to find the height of the kite from the ground.
Fro the right angled-triangle ABC, we have
[tex]\sin \angle BCA=\dfrac{AB}{AC}\\\\\\\Rightarrow \sin 53^\circ=\dfrac{p}{32}\\\\\\\Rightarrow p=32\times \sin 53^\circ\\\\\Rightarrow p=25.56.[/tex]
Since Sara is 5 feet tall, so the height of the kite from the ground is
AD = AB + BD = p + 25.56 = 5 + 25.56 = 30.56 feet.
Thus, the answer is 30.56 feet.
