Answered

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Jimoh walks 40 m up a hill which
slopes
at an angle of 20°
to the hori-
zontal. Calculate, correct to the nearest
metre, the:
a)
b)
horizontal distance covered
vertical height through which
he rises.
please solve it for me ​

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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