Lenny is planning to cut down a pine tree. He has parked his truck 90 feet away from the base of the tree and wants to make sure
that the tree will not hit his truck when it falls. The angle of elevation from the base of the truck to the top of the tree is 50°. How tall is the tree to the nearest foot? Should Lenny move his truck?
A)
58 feet; no
B)
69 feet; no
C)
75 feet; no
D)
107 feet; yes
A)
58 feet; no
B)
69 feet; no
C)
75 feet; no
D)
107 feet; yes
2 answers:
Answer:
D) 107 feet; yes
Step-by-step explanation:
Given :
Lenny has parked his truck 90 feet away from the base of the tree.
The angle of elevation from the base of the truck to the top of the tree is 50°
To Find: How tall is the tree to the nearest foot?
Solution :
Refer the attached figure
Since we are given that truck is 90 feet away from tree i.e. BC = 90 feet
The angle of elevation from the base of the truck to the top of the tree is 50° i.e. ∠ACB = 50°
Now to calculate the height of tree i.e. AB
Using trigonometric ratios :
Thus AB = 107.2578231≈107 feet
Hence , The height of tree is 107 feet
Yes, Lenny should move his truck .
Option D is correct.
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Answer:
From the graph: we have the coordinates of RST i.e,
R = (2,1) , S = (2,-2) , T = (-1,-2)
Also, it is given the scale factor and center of dilation C (1,-1)
The mapping rule for the center of dilation applied for the triangle as shown below:
or
or
Now,
for R = (2,1)
the image R' = or
⇒ R' =
For S = (2, -2) ,
the image S'= or
⇒ S' =
and For T = (-1, -2)
The image T' = or
⇒ T' =
Now, label the image of RST on the graph as shown below in the attachment:
