Question

Susie school is due west of her house into south of her friend Alana‘s house. The distance between the school and Alana‘s house is 5.6 miles in the straight line distance between Susie's house in Alanna‘s house is 8.7 miles. How far is Susie's house from school?

Answer 1

Answer: Susie's house is 6.9 miles from school

Explanation:

The distance between Susan's house, her school and Alana‘s house forms a right angle triangle. In the right angle triangle, the distance between Alana's house and the school represents the hypotenuse of the right angle triangle while the opposite and adjacent sides are the distances between Susie's house and her school and as well as the distance between Susie's house and Alana's house.

To determine the distance between Susie's house and her school h, we would apply Pythagoras theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

Therefore

8.7² = 5.6² + h²

h² = 75.69 - 31.36 = 44.33

h = √44.33

h = 6.9 miles

Answer 2

`\huge\boxed{√(44.33)\ \text{miles}\ (\approx 6.66\ \text{miles})}`

(See the attached diagram.)

We know one leg of a right triangle as well as its hypotenuse. We need to find the other leg using the Pythagorean Theorem.

The Pythagorean Theorem states that
`a^(2)+b^(2)=c^(2)`, where
`a` and
`b` are the legs and
`c` is the hypotenuse.

Insert the known values into the equation. The distance between Susie's house and the school will be represented by
`b`.

`5.6^(2)+b^(2)=8.7^(2)`

Convert the decimals to fractions.

`((28)/(5))^(2)+b^(2)=((87)/(10))^(2)`

To raise a fraction to a power, raise both the numerator and the denominator to that power.

`(784)/(25)+b^(2)=(7569)/(100)`

Multiply both sides of the equation by
`100`.

`3136+100b^(2)=7569`

Subtract
`3136` from both sides.

`100b^2=7569-3136`

Subtract.

`100b^(2)=4433`

Divide both sides by
`100`.

`b^(2)=44.33`

Take the square root of both sides.

`b=\boxed{√(44.33)\approx6.66}`