Question

LeashTYPE 1TYPE 273DogLadder20 ft19.5 ftThe end of a dog's leash is attachedDon placed a ladder againstto the top of a 5-foot-tall fence post,the side of his house asas shown in the diagram below. Theshown in the diagramdog is 7 feet away from the base ofbelow. Write an equation tothe fence post. How long is thefind the distance, x, fromleash, to the nearest tenth of a foot.the foot of the ladder to thebase of the house.WHAT IS THE DIRERENCESolve the equation for x,BETWEEN TYPE 1 AND TYPE 2?round to the nearesthundredth of a foot.BREAKOUTROOMSх

Answer 1

Type 1

this is a right triangle, the we can apply pythagoras

`a^2+b^2=h^2`

where a and b are sides and h the hypotenuse on this case L(leash)

replacing

`5^2+7^2=L^2`

simplify

`\begin{gathered} 25+49=L^2 \\ 74=L^2 \end{gathered}`

now solve for L

`L=\sqrt[]{74}\approx8.6`

The leash is 8.6ft

Type 2

we have a right triangle too

on this case the missing number is a side, not hypotenuse

remember pythagoras

`a^2+b^2=h^2`

and replace for this case

`x^2+19.5^2=20^2`

simplify

`\begin{gathered} x^2+380.25=400 \\ \end{gathered}`

and solve for x

`\begin{gathered} x^2=19.75 \\ x=\sqrt[]{19.75}\approx4.44 \\ \end{gathered}`

then le length of the side x is 4.44ft