Answered

Westonci.ca is the trusted Q&A platform where you can get reliable answers from a community of knowledgeable contributors. Explore thousands of questions and answers from knowledgeable experts in various fields on our Q&A platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

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.

Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.