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Your GPS shows that your friend’s house is 10.0 km away. But there is a big hill between your houses and you don’t want to bike there directly. You know your friend’s street is 6.0 km north of your street. How far do you have to ride before turning north to get to your friend’s house?

Respuesta :

okpalawalter8

Answer:

The value is [tex]c = 8 \ km [/tex]

Explanation:

From the question we are told that

The distance of friends house from your point is [tex]a = 10 \ km[/tex]

The distance of your friends street from your street is [tex]b = 6 \ km \ in the \ direction \ towards \ the \ north[/tex]

The diagram illustrating this question is shown on the first uploaded image

From the diagram we can apply by Pythagoras theorem as follows

[tex]a^2 = b^2 + c^2[/tex]

=>     [tex]c  =  \sqrt{^2 -  b^2}[/tex]

=>     [tex]c  =  \sqrt{ 10^2 -  6^2}[/tex]

=>     [tex]c  = 8 \  km [/tex]

Ver imagen okpalawalter8
Lanuel

By applying Pythagorean's theorem, you would have to ride a distance of 8 km before turning North, in order to get to your friend’s house.

How to determine the distance?

In order to determine the amount of distance that you would have to ride before turning North, we would apply Pythagorean's theorem.

From the question, we can deduce the following points:

  • Your friend’s house is the hypotenuse of the right-angle triangle (10.0 km).
  • Your friend’s street is opposite (North) your street (opposite of the right-angle triangle) i.e 6.0 km

Thus, we would have to find the adjacent side of the right-angle triangle.

Mathematically, Pythagorean's theorem is given by this formula:

x² + y² = z²

6² + y² = 10²

36 + y² = 100

y² = 100 - 36

y = √64

y = 8 km.

Read more on Pythagorean theorem here: https://brainly.com/question/23200848

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