A 25-foot ladder is propped up against a wall. The ladder is placed 7 feet from the base of the wall and reaches 24 feet up the wall, as shown in the figure. Which of the following equations could be solved to find 𝜃, the measure of the angle that the ladder makes with the ground?

To find the measure of the angle 𝜃 that the ladder makes with the ground, we can use trigonometric relationships. Given the information:

• The ladder is 25 feet long.
• The ladder is placed 7 feet from the base of the wall.
• The ladder reaches 24 feet up the wall.

We can use the cosine, sine, or tangent functions to find the angle 𝜃. Let's consider each option:

1. Cosine Function: The cosine of the angle 𝜃 is the ratio of the adjacent side (distance from the base of the wall) to the hypotenuse (length of the ladder). $\cos(𝜃) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{7}{25}$ Therefore, the equation to solve for 𝜃 is: $\cos(𝜃) = \frac{7}{25}$

2. Sine Function: The sine of the angle 𝜃 is the ratio of the opposite side (height up the wall) to the hypotenuse (length of the ladder). $\sin(𝜃) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{24}{25}$ Therefore, the equation to solve for 𝜃 is: $\sin(𝜃) = \frac{24}{25}$

3. Tangent Function: The tangent of the angle 𝜃 is the ratio of the opposite side (height up the wall) to the adjacent side (distance from the base of the wall). $\tan(𝜃) = \frac{\text{opposite}}{\text{adjacent}} = \frac{24}{7}$ Therefore, the equation to solve for 𝜃 is: $\tan(𝜃) = \frac{24}{7}$

Any of these equations could be used to find the measure of the angle 𝜃.