Question

a 12 foot ladder that is leaning against a house and makes a 75.5° angle with the level ground. which of the following equations can be used to determine the height, y, above the ground, in feet, that the ladder touches the house? (see yellow hint below.) cos75.5 = 12/y cos75.5 = y/12 sin75.5 = 12/y sin75.5 = y/12

Explanation:

Step1: Recall the definition of sine function

In a right - triangle, the sine of an angle \(\theta\) is defined as \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\).

Step2: Identify the sides and angle in the right - triangle

The ladder length is the hypotenuse (\(12\) feet), the height \(y\) is the side opposite to the angle \(75.5^{\circ}\).
So, \(\sin75.5^{\circ}=\frac{y}{12}\)

Answer:

\(\sin75.5=\frac{y}{12}\) (the fourth option)