To find the distance (d) the ladder goes up the wall, we can use trigonometry and the given information about the ladder's length and angle.
We can use the sine function to relate the angle and the side lengths of a right triangle:
sin(angle) = opposite/hypotenuse
In this case, the opposite side is the distance (d) the ladder goes up the wall, and the hypotenuse is the length of the ladder (13.5 m).
Let's calculate the value of sin(50° 17'):
sin(50° 17') = opposite/13.5
To find the value of sin(50° 17'), we can convert the angle from degrees, minutes, and seconds to decimal degrees.
Converting the minutes and seconds to decimal degrees:
0.17' = 0.17/60 ≈ 0.0028
0.0028° = 50.0028°
Now, we can calculate sin(50.0028°):
sin(50.0028°) = opposite/13.5
To isolate the value of opposite, we can rearrange the equation:
opposite = sin(50.0028°) * 13.5
Using a calculator, we find:
opposite ≈ 10.286 m
Therefore, the distance (d) the ladder goes up the wall is approximately 10.286 meters.