The bottom of the ladder rests on a horizontal flat surface and the top of the ladder rests against a wall. The ladder makes an angle of elevation of 61°. The bottom of the ladder is 6 ft from the base of the wall. How long is the ladder? Round your answer to the nearest foot. Do not include units
6/x = cos 61°
To find the length of the ladder, we can use trigonometric functions. In this case, we can use the sine function.
Step 1: Draw a diagram of the problem. Label the bottom of the ladder as the base, the top of the ladder as the opposite side, and the distance from the base of the wall to the ladder as the adjacent side.
Step 2: Identify the known values given in the problem. The angle of elevation is 61°, and the distance from the base of the wall to the ladder is 6 ft.
Step 3: Use the definition of sine to set up the equation. Sine is defined as the opposite divided by the hypotenuse.
sin(61°) = opposite / hypotenuse
Step 4: Substitute the known values into the equation.
sin(61°) = opposite / hypotenuse
sin(61°) = 6 / hypotenuse
Step 5: Solve for the hypotenuse (length of the ladder).
To solve the equation, we need to isolate the hypotenuse. We can do this by multiplying both sides of the equation by the hypotenuse.
hypotenuse * sin(61°) = 6
hypotenuse = 6 / sin(61°)
Step 6: Calculate the value of the hypotenuse using a calculator.
Using a calculator, we can find the value of sin(61°) to be approximately 0.8706.
hypotenuse = 6 / 0.8706
hypotenuse ≈ 6.89 ft
Step 7: Round the answer to the nearest foot.
The length of the ladder is approximately 6.89 feet. Rounded to the nearest foot, the length of the ladder is 7 feet.
Therefore, the length of the ladder is 7 ft.