Question

lesson 14 checkpoint catalina extends a ladder 15 feet and places it diagonally on a tree to get her cat that is perched on the lowest branch. which trigonometric ratio would she use to determine how high her cat was from the ground if the ladder formed a 65° angle with the ground? enter your answer as a single word (either sine, cosine, or tangent).

Explanation:

Step1: Recall trigonometric - ratio definitions

In a right - triangle formed by the ladder (hypotenuse), the height on the tree (opposite side to the angle with the ground), and the ground (adjacent side to the angle with the ground), we know that $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$, $\cos\theta = \frac{\text{adjacent}}{\text{hypotenuse}}$, and $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$.

Step2: Identify given values

We are given the length of the ladder (hypotenuse) $c = 15$ feet and the angle between the ladder and the ground $\theta = 65^{\circ}$, and we want to find the height $h$ (opposite side to the given angle). Since $\sin\theta=\frac{h}{c}$, we use the sine function.

Answer:

sine