Question

which equation can be used to find the measure of angle ljk?

\\(\sin(x) = \frac{10}{15}\\)

\\(\sin(x) = \frac{15}{10}\\)

\\(\cos(x) = \frac{10}{15}\\)

\\(\cos(x) = \frac{15}{10}\\)

Explanation:

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

Step 1: Identify the sides relative to angle x

• The angle of interest is \( \angle LJK \), labeled as \( x \).
• The side adjacent to angle \( x \) is \( LJ = 10\text{ in.} \).
• The hypotenuse (the side opposite the right angle \( \angle L \)) is \( KJ = 15\text{ in.} \).

Step 2: Choose the trigonometric ratio

• The cosine ratio relates the adjacent side to the hypotenuse:

$$ \cos(x) = \frac{\text{Adjacent}}{\text{Hypotenuse}} $$

Step 3: Set up the equation

• Substitute the known values into the ratio:

$$ \cos(x) = \frac{10}{15} $$

Answer:

$$ \cos(x) = \frac{10}{15} $$