Question

question 11
solve for x.
write your answers as a simplified radical and a decimal rounded to the nearest tenth. enter your answer as an equation, for instance x = your answer. if the answer is an integer value, leave the simplified radical box empty.
simplified radical:
decimal:

Explanation:

Step1: Identify adjacent side and hypotenuse

Adjacent side to 30°: $x$; Hypotenuse: 18 ft

Step2: Use cosine function

$\cos(30^\circ) = \frac{x}{18}$

Step3: Solve for x (radical)

$x = 18 \cdot \cos(30^\circ) = 18 \cdot \frac{\sqrt{3}}{2} = 9\sqrt{3}$

Step4: Calculate decimal value

$9\sqrt{3} \approx 9 \cdot 1.732 = 15.588 \approx 15.6$

Answer:

Simplified radical: $9\sqrt{3}$
Decimal: $15.6$