Final answer:
To determine the height the ladder reaches up the wall, use the sine of the given angle and the length of the ladder. The calculation is d = 14.5m * sin(54 degrees 44'), with the angle converted to decimal form for calculation purposes.
Step-by-step explanation:
To find the distance d that the ladder goes up the wall when it makes an angle of 54 degrees 44' with the horizontal, we can use the trigonometric function cosine (cos). We have a 14.5-meter ladder, and we want to find the opposite side of the right-angled triangle formed by the ladder, the wall, and the ground.
The cosine of an angle in a right-angled triangle is equal to the adjacent side (the distance from the base of the ladder to the wall) divided by the hypotenuse (the length of the ladder).
In this case, however, we need to use the sine function because we are looking for the distance up the wall, which is the opposite side. The sine of an angle is the opposite side over the hypotenuse:
sin(54 degrees 44') = d / 14.5m
To find out d, we rearrange the formula to solve for d by multiplying both sides by 14.5 meters:
d = 14.5m * sin(54 degrees 44')
Converting the angle to decimal form, which is typically required for calculators, we have 54.7333 degrees (where 44 minutes is approximately 0.7333 degrees).
We then calculate:
d = 14.5m * sin(54.7333 degrees)
After performing the calculation, you will get the value for d, which is the distance the ladder reaches up the wall.