Dionne is currently working with a client who is converting her G-shaped kitchen into an island kitchen. Right now, the distance between the client's stove and refrigerator is 2.6
meters, the distance between the stove and the sink is 1.46 meters, and the distance between the client's refrigerator and sink is 2.75 meters.
Use this information and what you know about the Law of Sines and the Law of Cosines to explore the questions below.
1. Sketch a diagram of the client's current kitchen. Be sure to label all the known information.
2. Which law should you use to find the measure of the angle that the refrigerator makes with the sink? Explain your choice.
3. Find all the angles in this work triangle. Show all of your calculations. Add the angle measures to the sketch you created in question 1.
4. What is the area of the client's current work triangle?
How do you know?
Column Break
The client says that she would like her appliances to be closer together in the new design. Dionne creates an island kitchen design where the distance between the stove and the sink is 1.3 meters and the distance between the sink and the refrigerator is 2.2 meters. The refrigerator makes a 31. 9°
angle with the stove.
5. Sketch a diagram of Dionne's design. Be sure to label all the known information.
6. Which law should you use to find the measure of the angle that the stove makes with the sink? Explain your choice.
7. Find all the missing measurements for the triangle that you sketched in question 5. Is more than one work triangle possible with these measurements? If so, sketch and label them completely. If not, explain why not.
8. Overall Dionne's client is happy with her design, but the client wonders if the distance between the refrigerator and the sink could be shortened to 1.35 meters if the other lengths and angle measures were allowed to remain the same. Is this possible? Explain why or why not.