Angie 1/3 = 0.3 mile
Blake 3/5 = 0.6 mile
Carlos 7/10 = 0.7 mile
Daisy 1/2 = 0.5 mile
answer:
Shortest Angie - 1/3 mile
Greatest Carlos - 7/10 mile
Answer:
AE=5 and EC=10
Step-by-step explanation:
Given : Suppose BE is an angle bisector of ΔABC , AB=9, BC=15, and AC=16
To find : AE and EC
Solution : BE form an angle bisector on line AC
Let AE=x and EC = y
Length of AC= AE+EC , putting values
16=x+y .....[1]
Now, we apply angle bisecor theorem which state that the ratio of the length of the line segment AE to the length of segment EC is equal to the ratio of the length of side AB to the length of side AC
![\frac{|AE|}{|EC|}=\frac{|AB|}{|AC|}](https://tex.z-dn.net/?f=%5Cfrac%7B%7CAE%7C%7D%7B%7CEC%7C%7D%3D%5Cfrac%7B%7CAB%7C%7D%7B%7CAC%7C%7D)
Put values,
![\frac{|x|}{|y|}=\frac{|9|}{|16|}](https://tex.z-dn.net/?f=%5Cfrac%7B%7Cx%7C%7D%7B%7Cy%7C%7D%3D%5Cfrac%7B%7C9%7C%7D%7B%7C16%7C%7D)
Cross multiply,
![\rightarrow 15x=9y](https://tex.z-dn.net/?f=%5Crightarrow%2015x%3D9y)
.......[2]
From [1] and [2]
Substitute x from [1] in [2], x= 16-y
![15(16-y)-9y=0](https://tex.z-dn.net/?f=15%2816-y%29-9y%3D0)
![\rightarrow 240-15y-9y=0](https://tex.z-dn.net/?f=%5Crightarrow%20240-15y-9y%3D0)
![\rightarrow 240=24y](https://tex.z-dn.net/?f=%5Crightarrow%20240%3D24y)
![\rightarrow y=10](https://tex.z-dn.net/?f=%5Crightarrow%20y%3D10)
Put y in value of x,
x= 16-y
x=16-10=6
Therefore, length of AE=x=5 and EC=y=10
Answer:
42° and 138°.
Step-by-step explanation:
Here we use the identity that
.
Now, to find
, we make use of the inverse sine function:
![x = sin^{-1}(0.0091)](https://tex.z-dn.net/?f=x%20%3D%20sin%5E%7B-1%7D%280.0091%29)
![\boxed{ x = 42^o.}](https://tex.z-dn.net/?f=%5Cboxed%7B%20x%20%3D%2042%5Eo.%7D)
Another solution to this is
Thus, the values of
in the interval
for which
are 42° and 138°.
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