Question

Lauren is about to eat a slice of pizza and is curious to see how large the crust is. The pizza slice has two sides that are 10 and 11 inches, and an angle in between the sides of 45 degrees. What is the length of the missing side (the crust)?

a) 5.5 inches
b) 7.8 inches
c) 10 inches
d) 12 inches

Answer 1

The length of the crust of a pizza slice with sides of 10 and 11 inches and a 45-degree angle in between can be calculated using the law of cosines, resulting in a length of approximately 7.8 inches.

Step-by-step explanation:

The student is asking to find the length of the crust of a pizza slice, which is the length of the side opposite the 45-degree angle of a right triangle with sides of 10 and 11 inches. This problem can be solved using the law of cosines:

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

Where:

• a and b are the lengths of the sides forming the angle C,
• C is the given angle,
• c is the length of the side opposite the angle C.

Plugging in the numbers, we get:

c^2 = 10^2 + 11^2 - 2(10)(11)cos(45 degrees)

Calculating further, we find that:

c^2 = 221 - 220*sqrt(2)/2

After calculating the square on both sides of the equation:

c ≈ 7.8 inches

Therefore, the length of the crust is approximately 7.8 inches, which corresponds to answer choice (b).