a ladder leaning against the wall makes an angel of 68 degrees with the level ground . the foot of the ladder is 3 ft away from the wall . how far up the wall does the ladder reach ?
why be a smartasss about it & it was my first time taking trig they told us do what we think we could solve
To find the distance the ladder reaches up the wall, we need to use trigonometric functions. The given information includes the angle (68 degrees) and the distance of the foot of the ladder from the wall (3 ft).
The trigonometric function that relates the angle, the length of the side opposite the angle (height up the wall), and the length of the side adjacent to the angle (distance from the foot of the ladder to the wall) is the tangent function.
Let's use the tangent function to solve this problem:
tan(angle) = opposite/adjacent
In this case:
tan(68 degrees) = height/3 ft
First, we need to find the value of tan(68 degrees). Using a scientific calculator or an online calculator, we can determine that tan(68 degrees) ≈ 2.74747741945462.
Now, we can solve for the height by rearranging the equation:
height = tan(68 degrees) x 3 ft
height ≈ 2.74747741945462 x 3 ft
height ≈ 8.24243225836386 ft
Therefore, the ladder reaches approximately 8.24 ft up the wall.
To solve this problem, you can use trigonometric functions, specifically the sine function, which relates the angle of a right triangle to the ratios of its sides.
Let's consider the ladder as the hypotenuse of a right triangle. The angle between the ladder and the ground is given as 68 degrees. The distance from the foot of the ladder to the wall is 3 feet. We want to find out how far up the wall the ladder reaches.
Using the sine function, we have:
sin(angle) = opposite / hypotenuse
In this case, the angle is 68 degrees, the opposite side is the distance up the wall, and the hypotenuse is the length of the ladder. Let's call the distance up the wall "x."
sin(68°) = x / 3
Now, we need to solve for x. Rearranging the equation, we have:
x = 3 * sin(68°)
Calculating this expression, we find:
x ≈ 2.80 feet
Therefore, the ladder reaches approximately 2.80 feet up the wall.
Did you draw a diagram? Review your basic trig functions? If so, then you can easily see that the height h can be found using
h/3 = tan68°