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Task: Trigonometric Equations Instructions Answer each part of the question. Complete each of the 2 activities for this Task. Activity 1 of 2 A 15-foot conveyor belt for raising and lowering supplies is leaning against a building at a 300 angle wit ha the ground, as shown. 1.5 teet 20 Which trigonometric equation could be used to find x, the distance, in feet, from the base of the conveyor belt to the building? O A. r15 sin 30° O B. x = 15 cos 30° o C. x x 15 Cos 30° O D. x = sin 30° 15 Activity 2 of 2 Use your equation from the previous question to solve for the value of x. Round to the nearest hundredth.

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Answers:

Activity 1.

x = 15 cos 30°

Activity 2.

x = 12.99

Explanation:

We can model the situation as:

Where the blue line is the conveyor belt and x is the distance from the base of the conveyor belt to the building.

Now, we need to find a trigonometric function that relates the adjacent side to the hypotenuse of an angle. So, we will use cosine because:

[tex]\cos \theta=\frac{Adjacent}{hypotenuse}[/tex]

Then, cos 30° is equal to:

[tex]\cos 30\text{ =}\frac{x}{15}[/tex]

So, solving for x, we get:

[tex]\begin{gathered} 15\cdot\cos 30=15\cdot\frac{x}{15} \\ 15\cdot\text{cos }30=x \end{gathered}[/tex]

Therefore, the value of x is:

x = 15 cos 30°

x = 12.99

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