A 15-foot ladder is resting against a wall and makes an angle of 48 degree's with the ground. Find the height to which the ladder will reach on the wall
The diagram is a right triangle, so the length of the ladder would be its hypotenuse, and the height of the wall, the opposite side of the angle of 48. Then
Sen 48= x / 15
Clear x and that's the answer.
To find the height to which the ladder will reach on the wall, we can use trigonometry. Specifically, we can use the sine function, since we have the angle and the length of the ladder.
The sine function is defined as the ratio of the length of the opposite side to the length of the hypotenuse in a right triangle. In this case, the wall forms the opposite side and the ladder forms the hypotenuse.
Let's denote the height to which the ladder reaches on the wall as "h". The length of the ladder is given as 15 feet, and the angle it makes with the ground is 48 degrees.
Using the sine function, we can write the following equation:
sin(48 degrees) = h / 15 feet
To find the value of "h", we rearrange the equation:
h = sin(48 degrees) * 15 feet
Now we can calculate the value of "h":
h ≈ 11.402 feet
Therefore, the ladder will reach a height of approximately 11.402 feet on the wall.