13. Ahmad is observing the islamic boarding school's mosque along with the minaret that nearby. The mosque and its minaret are 45m and 60m hig respectively. At that time the su elevation angle formed was 60°. The difference between the shadows of the minaret and mosque is
Jawaban:
We can start by drawing a diagram of the situation:
```
|
|\
| \
| \ 60°
| \
|____\
60m
---------------
45m
```
From the diagram, we can see that we have a right triangle with the minaret height (60m) as the opposite side and the distance between Ahmad and the base of the minaret (which we'll call x) as the adjacent side. We can use trigonometry to find x:
```
tan(60°) = opposite / adjacent
tan(60°) = 60 / x
x = 60 / tan(60°)
x = 34.64 (rounded to two decimal places)
```
Now we can find the length of the shadow of the minaret. We know that the angle of elevation of the sun is complementary to the angle of elevation of the minaret (since the sun's rays are parallel), so we can find the angle of elevation of the sun:
angle of elevation of sun = 90° - 60°
angle of elevation of sun = 30°
We also know that the length of the shadow of the minaret is directly proportional to the height of the minaret. Therefore:
length of shadow of minaret / minaret height = x / (x + 45)
Solving for the length of the shadow, we get:
length of shadow of minaret = minaret height * (x / (x + 45))
length of shadow of minaret = 60 * (34.64 / (34.64 + 45))
length of shadow of minaret = 32.14 (rounded to two decimal places)
Similarly, we can find the length of the shadow of the mosque. This time, the height we're using is 45m, and the distance from Ahmad to the base of the mosque is x + 45:
length of shadow of mosque / mosque height = (x + 45) / x
Solving for the length of the shadow, we get:
length of shadow of mosque = mosque height * ((x + 45) / x)
length of shadow of mosque = 45 * ((34.64 + 45) / 34.64)
length of shadow of mosque = 52.71 (rounded to two decimal places)
Finally, we can find the difference between the shadows of the minaret and mosque:
difference = length of shadow of mosque - length of shadow of minaret
difference = 52.71 - 32.14
difference = 20.57 (rounded to two decimal places)
Therefore, the difference between the shadows of the minaret and mosque is 20.57 meters.