Question

A 30-foot long escalator forms a 41° angle at the second floor. Which is the closest height of th

Answer 1

Answer:

$\huge\boxed{\text{B) } 22.5 \ \text{feet}}$

Step-by-step explanation:

We can use basic trigonometric functions to find the closest height of the escalator.

Let's set up a picture from what we already know. The length of the escalator is 30 feet, and it forms a 41 degree angle with the top. Since it will form a 90 degree angle with the ground, we can find the angle between the ground and the beginning of the escalator.

Since all triangles have an angle sum of 180:

• $90+41+x=180$
• $131+x=180$
• $x = 180-131$
• $x=49$

Now we know that the triangle looks something like this.

                   /  | 41°

                 /    |

               /      |

            /         |

30      /           |

       /              |                                                

     /                |

  /                   |

/__________| 90°

49°

We need to find the length of the side between the 41 and 90° angle.

To find which trigonometric operation to use on this triangle, we can use the acronym SOH CAH TOA.

Sine = Opposite / Hypotenuse

Cosine = Adjacent / Hypotenuse

Tangent = Opposite / Adjacent

We can use the sine of the 49 degree angle (opposite / hypotenuse) to find our missing side (since we know the hypotenuse).

Let's set up an equation and solve with our calculator.

• $\text{sin}(49) = \frac{\text{opposite}}{\text{hypotenuse}}$
• $\text{sin}(49) = \frac{x}{\text{30}}$
• $30 \cdot \text{sin}(49) = x$

We can calculate the sine of 49 with our calculator. We'd end up multiply 30 and that value and get 22.6.

Since the closest value to 22.6 on the answer choices is 22.5, the correct answer would be B) 22.5 feet.

Hope this helped!