Question

Most kitchens have a working triangle between the sink (s), the counter (c) and the oven (o). The distance between the sink and oven is 8 feet. The distance between the sink and counter is 6 feet and the distance between the oven and counter is 7 feet. In the kitchen triangle, where is the largest angle?.

Answer 1

Explanation:

To find the largest angle in the kitchen triangle, we can use the Law of Cosines. The Law of Cosines states that in any triangle with sides a, b, and c and opposite angles A, B, and C, the following relationship holds:

c^2 = a^2 + b^2 - 2ab * cos C

In the kitchen triangle, we have the sides a = 6, b = 7, and c = 8. We can use the Law of Cosines to find the cosine of each angle and then use the inverse cosine function to find the angles themselves:

cos A = (b^2 + c^2 - a^2) / (2bc) = (7^2 + 8^2 - 6^2) / (2 * 7 * 8) = 0.41

A = cos^-1(0.41) = 61.8°

cos B = (a^2 + c^2 - b^2) / (2ac) = (6^2 + 8^2 - 7^2) / (2 * 6 * 8) = 0.95

B = cos^-1(0.95) = 18.4°

cos C = (a^2 + b^2 - c^2) / (2ab) = (6^2 + 7^2 - 8^2) / (2 * 6 * 7) = -0.15

C = cos^-1(-0.15) = 120.0°

The largest angle in the kitchen triangle is C, which measures 120.0°.