Question

Camp Sunshine is on the lake. Use the Pythagorean Theorem to find the distance between Francesca's house and Camp Sunshine to the nearest tenth of a meter. Camp Sunshine (190, 130) House (10,20) (190, 20) The distance between Francesca's house and Camp Sunshine is approximately meters.

Answer 1

The distance between Francesca's house and camp sunshine is approximately 211 meters

Here, we want to calculate the distance between the house and camp

From what we have in the diagram, we can see a right angled triangle

The distance we want to calculate represents the hypotenuse of the triangle

Thus, we need the measures of the distance of the two other sides

These are the distances between camp sunshine and the third side; and also the distance between the house and the third side

To calculate this, we will use the distance formula

a) Third side and camp sunshine

`\begin{gathered} D\text{ = }\sqrt[]{(_{}x_2-x_1)^2+(y_2-y_1)^2} \\ (x_1,y_1)\text{ = (190,130)} \\ (x_2,y_2)\text{ = (190,20)} \\ D\text{ = }\sqrt[]{(190-190)^2+(20-130)^2} \\ D\text{ = }\sqrt[]{(-110)^2} \\ D\text{ = 110 meters} \end{gathered}`

b) Third side and the house

`\begin{gathered} D\text{ = }\sqrt[]{(_{}x_2-x_1)^2+(y_2-y_1)^2} \\ (x_1,y_1)\text{ = (190,20)} \\ (x_2,y_2)\text{ = ( }10,20) \\ D\text{ = }\sqrt[]{(10-190)^2+(20-20)^2} \\ D\text{ = }\sqrt[]{(-180)^2} \\ D\text{ = 180 meters} \end{gathered}`

Thus, we are to apply the Pythagoras' theorem to these side lengths. The Pythagoras' theoresm states that the sqaure of the length of the hypotenuse equals the sum of the squares of the lengths of the two other sides

What we want to calculate here is the hypotenuse

Thus, applying the rule, we have that;

`\begin{gathered} D^2=110^2+180^2 \\ D^2\text{= 44,500} \\ D\text{ }=\text{ }\sqrt[]{44,500} \\ D\text{ = 210.95 } \\ D\text{ = 211 meters} \end{gathered}`