Question

1. An awning that covers a sliding glass door that is 88 inches tall forms an angle of 50' with the wall.

The purpose of the awning is to prevent sunlight from entering the house when the angle of elevation
of the Sun is more than 65'. See the figure. Find the length of L of the awning. Round to the nearest
Inch.

Answer 1

To calculate the length of the awning, we can use the law of cosines. The law of cosines states that in a triangle, the sum of the squares of the lengths of two sides is equal to the square of the length of the third side. In this case, we can let the angle of elevation of the sun be A, the length of the awning be L, and the angle formed by the awning and the wall be B. We then have:

L^2 = 88^2 + (65 * tan(A))^2 - 2(88)(65 * tan(A))cos(B)

Substituting in the given values for A, B, and L, we get:

L^2 = 88^2 + (65 * tan(65))^2 - 2(88)(65 * tan(65))cos(50)

Solving for L, we get a value of L = 103.9 inches. Rounding to the nearest inch, the length of the awning is 104 inches.