Question

kitchen triangle in exercises 27 and 28, use the following information. the term “kitchen triangle” refers to the imaginary triangle formed by three kitchen appliances: the refrigerator, the sink, and the range. the distances shown are measured in feet. 27. what is wrong with the labels on the kitchen triangle?

Explanation:

Step1: Check the triangle angle - sum property

The sum of interior angles of a triangle is \(180^{\circ}\).

Step2: Calculate the sum of given angles

\(30^{\circ}+70^{\circ}+80^{\circ}=180^{\circ}\)

Step3: Apply the Law of Sines

The Law of Sines states that \(\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}\). Let \(a = 4\), \(b = 6\), \(c = 8\), \(A = 30^{\circ}\), \(B = 70^{\circ}\), \(C = 80^{\circ}\).
\(\frac{4}{\sin30^{\circ}}=\frac{4}{0.5}=8\), \(\frac{6}{\sin70^{\circ}}\approx\frac{6}{0.9397}\approx6.38\), \(\frac{8}{\sin80^{\circ}}\approx\frac{8}{0.9848}\approx8.12\)
Since \(\frac{4}{\sin30^{\circ}}
eq\frac{6}{\sin70^{\circ}}
eq\frac{8}{\sin80^{\circ}}\), the side - angle relationships are incorrect.

Answer:

The side - angle relationships do not follow the Law of Sines.