Modeling Real Life: Finding the Height of a Sail
Calculating the Height of the Sail
The area of a sail is 40(1)/(2) square feet. The base and the height of the sail are equal. What is the height of the sail (in feet)?
By using the area formula for a triangle and given that the sail's base and height are equal, solving for the height yields 9 feet.
Explanation:Given that the area of the sail is 40(1)/(2) square feet and that the sail's base and height are equal, we can use the formula for the area of a triangle (A = 1/2 x base x height) to find the height of the sail. Let's denote the height of the sail as h:
40(1)/(2) = 1/2 x h x h
Simplifying the equation, we get:
h² = 81
Taking the square root of both sides, we find:
h = 9
So, the height of the sail is 9 feet. Since the base and height are equal, the height is also the length of the base.
In this real-life modeling scenario, we've used basic geometry principles to solve for the height of the sail. The sail's area and the information about its base and height relationship allow us to set up an equation and solve for the height. This type of problem-solving is common in various fields, such as engineering and architecture, where practical applications of geometry play a significant role in designing and understanding physical structures.
MODELING REAL LIFE The area of a sail is 40(1)/(2) square feet. The base and the height of the sail are equal. What is the height of the sail (in feet )? By using the area formula for a triangle and given that the sail's base and height are equal, solving for the height yields 9 feet. Explanation: Given that the area of the sail is 40(1)/(2) square feet and that the sail's base and height are equal, we can use the formula for the area of a triangle (A = 1/2 x base x height) to find the height of the sail. Let's denote the height of the sail as h: 40(1)/(2) = 1/2 x h x h Simplifying the equation, we get: h² = 81 Taking the square root of both sides, we find: h = 9 So, the height of the sail is 9 feet. Since the base and height are equal, the height is also the length of the base. In this real-life modeling scenario, we've used basic geometry principles to solve for the height of the sail. The sail's area and the information about its base and height relationship allow us to set up an equation and solve for the height. This type of problem-solving is common in various fields, such as engineering and architecture, where practical applications of geometry play a significant role in designing and understanding physical structures.