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Sagot :
Step-by-step explanation:
A new approach!
Given:
* Jimoh walks 40 m 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
This problem can be solved using the Pythagorean theorem (b² = a² + c²). Since the slope is 20°, we can draw a right triangle with the horizontal distance as the base (a), the vertical height as the height (c), and the hypotenuse (b) as the total distance (40 m).
Let's define the variables:
* a = horizontal distance (in meters)
* c = vertical height (in meters)
* b = total distance (in meters)
We can set up the equation:
b² = a² + c²
Since b = 40 m, we can rewrite the equation as:
40² = a² + c²
1600 = a² + c²
Now, we need to find a and c. We can use the tangent function to relate the angle to the ratio of a and c:
tan(20°) = c / a
Converting the angle to radians:
tan(π/9) = c / a
Simplifying the equation, we get:
a ≈ 28.28 meters
c ≈ 18.57 meters
So, the horizontal distance covered is approximately 28.28 meters.
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.
I hope this solution meets your requirements
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