Question

alexas friends got her a skydiving lesson for her birthday. her helicopter took off from the skydiving center, ascending in an angle of \\(20^{\circ}\\), and traveled a distance of \\(3.4\\) kilometers before she fell in a straight line perpendicular to the ground.

write the equation to solve for \\(x\\).

how far from the skydiving center did alexa land? round your final answer to the nearest tenth.

alexa landed kilometers from the skydiving center.

Explanation:

⚡ Using what you learned: right triangle trigonometry (soh cah toa)

Step 1: Identify the trigonometric ratio

We have a right triangle where:

• The angle of elevation is \( 20^{\circ} \).
• The hypotenuse is \( 3.4\text{ km} \).
• The adjacent side to the angle is \( x \).

Using the cosine ratio:

$$ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} $$

$$ \cos(20^{\circ}) = \frac{x}{3.4} $$

Step 2: Solve for \( x \)

Multiply both sides by \( 3.4 \):

$$ x = 3.4 \cdot \cos(20^{\circ}) $$

$$ x \approx 3.4 \cdot 0.9397 $$

$$ x \approx 3.195 $$

Rounding to the nearest tenth:

$$ x \approx 3.2\text{ km} $$

Answer:

Equation to solve for \( x \):

$$ \cos(20^{\circ}) = \frac{x}{3.4} $$

Distance Alexa landed:
Alexa landed 3.2 kilometers from the skydiving center.