Final answer:
The length of each guy wire for Deandra's Santa display is approximately 28.82 feet, calculated using the tangent of the given 48° angle with the ground and the height of the Santa.
Step-by-step explanation:
To find the length of each guy wire that Deandra needs for his Santa display, we can apply trigonometry, specifically the tangent function. The guy wires make a 48° angle with the ground and are attached to the top of a 32 ft tall Santa. To find the length of the guy wire, we use the formula:
L = height / tan(angle)
Where L is the length of the wire, height is the height of the Santa, and tan(angle) is the tangent of the guy wire's angle with the ground.
Plugging in the values, we get:
L = 32 ft / tan(48°)
First, we calculate the tangent of 48°:
tan(48°) ≈ 1.1106
Then, we can find the length:
L ≈ 32 ft / 1.1106 ≈ 28.82 ft
So, each guy wire needs to be approximately 28.82 feet long to securely display the Santa.