A laffer leaning against a house maes an angle of 60 degress with the ground. The foot of the leadder is 7 feet from the foundation of the house. How long is the ladder? Please help.

Solved under a previous post.

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To solve this problem, we can use trigonometric ratios from right triangles, specifically the sine function. The sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse.

In this case, the ladder is the hypotenuse of the right triangle formed by the ladder, the ground, and the line from the foot of the ladder to the house. Let's assume the length of the ladder is "x".

We know that the angle between the ladder and the ground is 60 degrees, and the length of the side adjacent to this angle (the distance from the foot of the ladder to the house) is 7 feet.

Using the sine function, we can set up the following equation:

sin(60 degrees) = opposite/hypotenuse

sin(60 degrees) = 7/x

To find the length of the ladder, we can rearrange the equation and solve for x:

x = 7/sin(60 degrees)

Using a scientific calculator or trigonometric table, the sine of 60 degrees is approximately 0.866.

Therefore, the length of the ladder is:

x = 7 / 0.866 ≈ 8.08 feet

So, the ladder is approximately 8.08 feet long.