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Sagot :
Step-by-step explanation:
Let's break it down step by step!
Given:
* Jimoh walks 40 meters up a hill
* The slope is 20° to the horizontal
* We need to find:
+ a) The horizontal distance covered
+ b) The vertical height through which he rises
To solve this, we can use the concept of trigonometry. Since the slope is 20°, we can use the tangent function to relate the angle to the ratio of the horizontal and vertical distances.
Let's define the variables:
* h = horizontal distance (in meters)
* v = vertical height (in meters)
* θ = angle of the slope (in radians)
We can use the tangent function to relate h and v:
tan(θ) = v / h
Since θ is 20°, we can convert it to radians:
θ = 20° × (π/180) = π/9
Now, substitute the values:
tan(π/9) = v / h
Simplifying the equation, we get:
h ≈ √((40)^2 / (1 - (1 - (π/9)^2)))
Simplifying further, we get:
h ≈ 28.28 meters
So, the horizontal distance covered is approximately 28.28 meters.
Now, let's find the vertical height through which Jimoh rises. We can use the equation:
v = h × tan(θ)
Substituting the values, we get:
v = 28.28 × tan(π/9)
≈ 28.28 × 0.654
≈ 18.57 meters
So, the vertical height through which Jimoh rises is approximately 18.57 meters.
Rounded to the nearest meter, the answers are:
a) The horizontal distance covered is approximately 28 meters.
b) The vertical height through which he rises is approximately 19 meters.
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