Question

ben and emma are out flying a kite. emma can see that the kite string she is holding is making a \\(70^\circ\\) angle with the ground. ben is standing 50 feet away. to the nearest foot, how many feet of string has emma let out?

complete the trig ratio.

\\(\text{___ } 70^\circ = \frac{\text{___}}{\text{___}}\\)

write your answer as a decimal rounded to the nearest hundredth.

emma has let out approximately \\(\text{___}\\) feet of string.

Explanation:

Set up the trigonometric ratio

$$ \cos(70^\circ) = \frac{\text{Adjacent}}{\text{Hypotenuse}} = \frac{50}{x} $$

Solve for the unknown length

$$ x = \frac{50}{\cos(70^\circ)} $$

Calculate the numerical value

$$ x \approx \frac{50}{0.34202} \approx 146.19 $$

Answer:

Question 1

<blank>\(\cos\)</blank> \(70^\circ =\) <blank>\(\frac{50}{x}\)</blank>

Question 2

Emma has let out approximately <blank>146.19</blank> feet of string.