Question

You are building a house and are making a drawing of the kitchen. the sink is 3 feet away from the dishwasher, and the sink is 8 feet away from the fridge. the included angle between the distances is 48°. how far away is the dishwasher from the fridge? explain. are these reasonable dimensions for a kitchen? if not, what would you change?

Answer 1

Consider the triangle with vertices S (sink), D (dishwasher) and F (fridge). From the conditions data SD=3, SF=8 and ∠S=48°.

Use the cosine theorem to find unknown distance:

$FD^2=SD^2+SF^2-2SD\cdot SF\cdot \cos S$,

$FD^2=3^2+8^2-2\cdot 3\cdot 8\cdot \cos 48^{\circ},\\ FD^2=9+64-48\cdot 0.67,\\ FD^2=40.84, \\ FD=\sqrt{40.84}, \\ FD=6.39$ feet.

Then the distance between dishwasher and fridge is 6.39 feet.

Are these dimensions reasonable is up to kitchen owner))