while standing at the left corner of the schoolyard in front of her school, Suzie estimates that the front face is 8.9m wide and 4.7m high. from her position, Suzie is 12m from the base of the right exterior wall. she determines that the left and right exterior walls appearto ne 39 degrees apart. From her position, what is the angle of elevation, to the nearest degree, to the top of the left exterior wall?
from her feet, or eyes?
Too many unknowns.
What shape is the schoolyard?
Does it extend beyond the side walls of the school?
Can't see what the left corner has to do with anything.
There's a whole circle of points that are 12m from the front base of the right wall.
Draw a diagram, label all corners of the school, label Suzie's positions, so we can fix them in our mind.
Then come on back. Who knows, the systematic labeling of the diagram may show how it can be solved...
To determine the angle of elevation to the top of the left exterior wall, we can use trigonometry and some basic geometric concepts.
First, let's visualize the situation. Imagine standing at the left corner of the schoolyard, facing the school. Suzie estimates that the front face of the school (the distance between the left and right exterior walls) is 8.9m wide and 4.7m high. Suzie is standing 12m from the base of the right exterior wall, and she determines that the left and right exterior walls appear to be 39 degrees apart.
Now, let's draw a diagram to better understand the situation:
```
|
|
|
4.7m |
______
| /|
| / |
| / |
| / |
| / |8.9m
| / |
|/______|
X
```
In this diagram, the vertical line represents the left exterior wall, and the diagonal line represents the front face of the school. The horizontal line represents the distance from Suzie's position to the base of the right exterior wall.
To find the angle of elevation to the top of the left exterior wall, we can use the tangent function:
tan(angle) = opposite/adjacent
In this case, the opposite side is the height of the left exterior wall (4.7m), and the adjacent side is the distance from Suzie's position to the base of the right exterior wall (12m).
So, we can calculate the angle of elevation as follows:
angle = arctan(opposite/adjacent) = arctan(4.7/12)
Using a scientific calculator or a trigonometric table, we can find the inverse tangent of 4.7/12 to get the angle in radians. Finally, we can convert the angle to degrees by multiplying it by 180/π.
angle = arctan(4.7/12) * 180/π
By evaluating this expression, we will get the angle of elevation to the top of the left exterior wall in degrees, rounded to the nearest degree.