A 15 FOOT LADDER MAKES 52 DEGREES ANGLE WITH THE GROUND.HOW FAR WILL THE TOP OF THE LADDER BE ABOVE THE GROUND?
h/15 = sin52
solve for h
To find out how far the top of the ladder will be above the ground, we can use trigonometry and the given angle.
First, let's label the triangle formed by the ladder, the ground, and the distance between the ladder's base and the point where it touches the ground. Let's call this distance 'x'. The height of the ladder above the ground is the side opposite the angle, and the ladder itself is the hypotenuse.
Now, we can use the trigonometric function called sine to find the height. The sine of an angle is equal to the ratio of the length of the side opposite the angle to the length of the hypotenuse.
In this case, the sine of the angle can be written as sin(52°), and the ratio can be written as opposite (height) / hypotenuse (ladder length).
Therefore, we have the equation: sin(52°) = height / 15ft.
To find the value of sin(52°), you can use a scientific calculator or an online calculator. The approximate value of sin(52°) is 0.788.
Now, we can solve for the height of the ladder above the ground:
0.788 = height / 15ft.
To isolate the height, we can multiply both sides of the equation by 15ft:
0.788 * 15ft = height.
Now, calculate the height:
11.82ft = height.
So, the top of the ladder will be approximately 11.82 feet above the ground.
To find out how far the top of the ladder will be above the ground, you can use the trigonometric function sine.
The angle between the ladder and the ground is given as 52 degrees, and the length of the ladder is 15 feet. Let's call the height above the ground "h".
Step 1: Convert the angle from degrees to radians by multiplying it by π/180:
52 degrees * (π/180) = 0.9076 radians (rounded to four decimal places).
Step 2: Use the sine function to calculate the height above the ground:
sin(0.9076) = h/15 feet.
Step 3: Rearrange the equation to solve for h:
h = 15 feet * sin(0.9076).
Using a scientific calculator or an online calculator, evaluate sin(0.9076) to find the value of h.