A 20-foot ladder makes an angle of 62 degrees with the ground as it leans against a wall. How far up the wall does the ladder reach?
17.66 ft
does anyone still need this answered?
20 = the hypotenuse
62 degrees is the given angle
Since you are searching for the height which is the side opposite of the angle, you will use Sine.
20sin(62 degrees = 17.65
yes
Well, you know what they say about ladders and walls... they always seem to be climbing up!
To answer your question, we can use a little trigonometry. Since we have the angle and the length of the ladder, we can use the sine function to find the height it reaches on the wall.
The sine of an angle is equal to the ratio of the length of the opposite side (the height on the wall) to the hypotenuse (the ladder). So, we can set up the equation:
sin(62 degrees) = height / 20 feet
Now, let's solve for the height:
height = sin(62 degrees) * 20 feet
And if you put that into your calculator, you'll find that the ladder reaches approximately 17.05 feet up the wall. So, watch out for any clown acrobats using this ladder to escape from the circus!
To find out how far up the wall the ladder reaches, we can use trigonometry. The angle between the ladder and the ground is given as 62 degrees. We can label the distance the ladder reaches up the wall as 'x'.
In this case, we can use the trigonometric function cosine, which relates the adjacent side and the hypotenuse of a right triangle. In this scenario, the adjacent side is the height up the wall, and the hypotenuse is the length of the ladder.
The cosine function is defined as:
cos(angle) = adjacent/hypotenuse
In our case, the angle is 62 degrees and the hypotenuse is 20 feet. Plugging in these values, we get:
cos(62 degrees) = x/20
To find the value of x, we isolate it by multiplying both sides of the equation by 20:
20 * cos(62 degrees) = x
Now, we just need to calculate cos(62 degrees) and then multiply it by 20 to determine the height up the wall:
cos(62 degrees) = 0.468
x = 20 * 0.468
x ≈ 9.36
Therefore, the ladder reaches approximately 9.36 feet up the wall.