Answer:
[tex]x \approx 86.5[/tex]
Step-by-step explanation:
To solve the given problem, use the following trigonometric ratios,
[tex]sin(\theta) = \frac{opposite}{hypotenuse}\\\\cos(\theta) = \frac{adjacnet}{hypotenuse}\\\\tam(\theta) = \frac{opposite}{adjacent}[/tex]
Each of the sides are named relative to the given angle, therefore, when looking at different angles, the sides will have different names. In this case, one is given the length of the hypotenuse, and one is asked to find the length of the given side. Therefore, it would make the most sense to use the ratio of sine ([tex]sin[/tex]). Substitute in the given values and solve,
[tex]sin(84)=\frac{x}{87}[/tex]
Manipulate the equation so that it is solved for (x),
[tex]x=(87(sin(84))[/tex]
Solve,
[tex]x \approx 86.5[/tex]
