In a mall, a shopper rides up an escalator between floors. at the top of the escalator, the shopper turns right and walks 9.09 m
to a store. the magnitude of the shopper's displacement from the bottom of the escalator to the store is 16.0 m. the vertical distance between the floors is 4.89 m. at what angle is the escalator inclined above the horizontal?
1 answer:
Let x represent the horizontal displacement of the top of the escalator from its bottom. The geometry of the problem and the Pythagorean theorem tell you
x² + 4.89² + 9.09² = 16.0²
x² = 149.4598
x ≈ 12.22 . . . meters
Then the tangent of the angle of interest is
tan(α) = (4.89 m)/(12.22 m)
α = arctan(4.89/12.22) ≈ 21.8°
The escalator is inclined 21.8° above the horizontal.
x² + 4.89² + 9.09² = 16.0²
x² = 149.4598
x ≈ 12.22 . . . meters
Then the tangent of the angle of interest is
tan(α) = (4.89 m)/(12.22 m)
α = arctan(4.89/12.22) ≈ 21.8°
The escalator is inclined 21.8° above the horizontal.
You might be interested in
There will be 72 flowers in total in the large arrangement.
Step-by-step explanation:
No. of red flowers in vase = 4
No. of white flowers in vase = 5
Ratio of red flowers to white flowers = 4:5
No. of red flowers in large arrangement = 32
No. of white flowers in large arrangement = w
Ratio of red flowers to white flowers = 32:w
Using proportion;
Ratio of red flowers to white flowers :: Ratio of red flowers to white flowers
Product of extreme = Product of mean
Dividing both sides by 4
Total flowers in large arrangement = Red flowers + white flowers
Total flowers in large arrangement = 32 + 40 =72
There will be 72 flowers in total in the large arrangement.
Keywords: ratio, proportion
Learn more about ratios at:
#LearnwithBrainly