Question

Amanda's school is due west of her house and due south of her friend Shereen's house. The distance between the school and Shereen's house is 2 kilometers and the straight-line distance between Amanda's house and Shereen's house is 7 kilometers. How far is Amanda's house from school? If necessary, round to the nearest tenth.

Answer 1

The Amanda's house is 6.7 km far from her school.

Explanation:

From the given information,

• The Amanda's school is due west of her house forms the base.
• The school is due south of the Shereen's house forms the height.
• The straight-line distance between Amanda's house and Shereen's house forms the hypotenuse.

Therefore, It can be determined that it forms the right angle triangle.

It is given that,

The distance between the school and Shereen's house is 2 kilometers.

That is, the height of the triangle = 2 km

The straight-line distance between Amanda's house and Shereen's house is 7 kilometers.

That is, the hypotenuse of the triangle = 7 km

Now, the distance between the Amanda's house and her school is the base of the triangle.

To find the base :

Base =
`\sqrt{(hypotenuse)^(2)-(height)^(2) }`

⇒
`\sqrt{(7)^(2) -(2)^(2) }`

⇒
`√(49-4)`

⇒
`√(45)`

⇒ 6.7 km

Therefore, the Amanda's house is 6.7 km far from her school.