a tree casts a shadow 8 feet long. A 6-foot Man cast a shadow 4 feet long. The triangle formed by the tree and its shadow is sim
ilar to the triangle formed by the man and his shadow. How tall is the tree?
1 answer:
Answer:
12 feet
Step-by-step explanation:
Draw a diagram (see picture below). The tree and its shadow is one triangle, the man and its shadow is another triangle. We assume both are right triangles because people and trees stand vertical.
Create a proportion to solve. Put the missing value in a numerator.
Tree height / Tree shadow = Man height / Man shadow
Solve using cross multiplication. Multiply x by 4. Multiply 6 by 8.
4x = 48 Divide both sides by 4 to isolate x.
x = 12 Height of tree
The tree is 12 feet tall.
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Answer:
21) falls
22) vertical
23) rises
24) rises
25) falls
26) horizontal
27) rises
28) horizontal
29) falls
Step-by-step explanation:
We shall use the slope formula to calculate the slopes of the line passing through each pair of point.
21: (3,1), (2,6)
The slope is
.
A negative slope means this line falls
22) (-2,5), (-2,4)
The slope is = undefined
An undefined slope means this line is vertical
23) The given point is (0,8) (2,10)
The slope is
A positive slope means this line rises
24) The points are (-3,-3), (3,1)
The slope is
A positive slope means this line rises
25) The points are: (5,0) (6,-2)
Slope:
A negative slope means this line falls
26) The points are (-2,-8) , (5,-8).
Slope:
A zero slope means this line is horizontal
27) The points are: (-1,2) , (5,3)
Slope:
A positive slope means this line rises
28) The points are: , (-1,4)
Slope:
A zero slope means the line is horizontal
29) The points are:
Slope:
A negative slope means this line falls.