A ladder leaning against a house makes an angle of 60 degress with the ground. The foot of the ladder is 7 feet from the foundation of the house.how long is the ladder?
please some sugesstions
Draw a rt. triangle with the hyp representing the ladder, anbd the hor side equals 7ft.
L = 7 / cos60 = 14 ft. = Length of
ladder.
To find the length of the ladder, we can use trigonometric functions, specifically the sine function. Here's how you can solve it:
1. Draw a diagram: Sketch a right triangle, where one angle (the one formed by the ladder and the ground) is 60 degrees. Label the sides of the triangle: the side opposite the 60-degree angle as "opposite" (representing the height of the ladder), the side adjacent to the 60-degree angle as "adjacent" (representing the distance from the foot of the ladder to the house), and the hypotenuse as "ladder" (the length we want to find).
2. Apply the sine function: In a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the hypotenuse. So, we have sin(60 degrees) = opposite / ladder.
3. Substitute known values: We know that the ladder's foot is 7 feet from the house, so the length of the adjacent side is 7 feet. We also know that sin(60 degrees) equals √3 / 2.
4. Solve for the ladder: Rearrange the equation from step 2 to solve for the ladder: ladder = opposite / sin(60 degrees). Plug in the values: ladder = 7 / (√3 / 2).
5. Simplify the equation: To divide by a fraction, multiply by its reciprocal. So, ladder = 7 * (2 / √3).
6. Rationalize the denominator: To rationalize the denominator (i.e., eliminate the square root), multiply both the numerator and the denominator by the conjugate of the denominator. In this case, multiply both sides of the equation by (√3 / √3): ladder = 7 * (2 / √3) * (√3 / √3). Simplify to ladder = 14√3 / 3.
Therefore, the length of the ladder is approximately 14√3 / 3 feet.