Question

1. which trig ratio would you use to solve for the missing side?

a) sine
b) cosine
c) tangent

1. which trig ratio would you use to solve for the missing side?

a) sine
b) cosine
c) tangent

Explanation:

Step1: Recall trig - ratio definitions

Sine is $\sin\theta=\frac{opposite}{hypotenuse}$, Cosine is $\cos\theta = \frac{adjacent}{hypotenuse}$, Tangent is $\tan\theta=\frac{opposite}{adjacent}$.

Step2: Analyze the first triangle

In the first triangle, if we want to solve for the missing side and we know an angle and a side - length, we need to consider the position of the known and unknown sides relative to the given angle. Since we don't know which side is missing, but if we assume we are working with the angle $\theta = 50^{\circ}$ and the side of length $10$ m. If the missing side is opposite the given angle and we know the hypotenuse (or vice - versa), we use sine. If the missing side is adjacent to the given angle and we know the hypotenuse (or vice - versa), we use cosine. If the missing side is opposite and the known side is adjacent (or vice - versa) to the given angle, we use tangent. Without more information about which side is missing, we can't be sure, but if we assume we want to find the side opposite the $50^{\circ}$ angle and we know the adjacent side, we use tangent.

Step3: Analyze the second triangle

Similarly, for the second triangle, with an angle (not given in the problem statement but assuming we have one) and two side - lengths $7$ m and $15$ m. If we want to find the side opposite an angle and we know the adjacent side, we use tangent. If we want to find the side relative to the hypotenuse (either adjacent or opposite), we use sine or cosine. Without knowing which side is missing and the angle, if we assume we are relating the opposite and adjacent sides of a non - right angle, we use tangent.

Answer:

1. c) Tangent
2. c) Tangent