Question

hudson is painting the outside of a building. his ladder can reach the second-floor balcony, which is 11 m high. how long is his ladder?
complete the trig ratio. use x as your variable.

\underline{\quad\quad}(58^{\circ}) = \frac{\underline{\quad\quad}}{\underline{\quad\quad}}

Explanation:

⚡ Using what you learned: introduction to trigonometric functions

Step 1: Identify the parts of the right triangle

The ladder, the ground, and the side of the building form a right triangle:

• The angle of elevation from the ground to the ladder is \( 58^{\circ} \).
• The side opposite to the \( 58^{\circ} \) angle is the height of the balcony, which is \( 11\text{ m} \).
• The hypotenuse of the right triangle is the length of the ladder, represented by the variable \( x \).

Step 2: Choose the correct trigonometric ratio

The trigonometric ratio that relates the opposite side and the hypotenuse is the sine function:

$$ \sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}} $$

Step 3: Set up the equation

Substitute the known values into the sine ratio:

$$ \sin(58^{\circ}) = \frac{11}{x} $$

Answer:

The completed trigonometric ratio is:

$$ \sin(58^{\circ}) = \frac{11}{x} $$

In the input boxes:

• Left box: sin
• Top right box: 11
• Bottom right box: x