Triangle town wants to build a school that is equidistant from its three cities L, M, and N. Which construction correctly finds
the best location of the school?
Option choices are...
A. Construction Y because point E is the incenter of ΔLMN
B. Construction Y because point E is the circumcenter of ΔLMN
C. Construction X because point C is the incenter of ΔLMN
D. Construction X because point C is the circumcenter of ΔLMN
Option choices are...
A. Construction Y because point E is the incenter of ΔLMN
B. Construction Y because point E is the circumcenter of ΔLMN
C. Construction X because point C is the incenter of ΔLMN
D. Construction X because point C is the circumcenter of ΔLMN
1 answer:
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Answer:
option D is true.
Step-by-step explanation:
The right-angled triangle is shown.
From the right-angled triangle,
The angle Ф = 60°
We know that the trigonometric ratio
tan Ф = opposite / adjacent
- opposite = 4
- adjacent = n
Thus,
tan 60 = 4 / n
√3 = 4/n
n = 4/√3
Thus,
n = 4/√3
= (4 × √3) / (√3 × √3)
= 4√3 / 3
Thus,
n = 4√3 / 3
Using Pythagorean theorem
m = √n²+4²
Thus,
- n = 4√3 / 3
Therefore, option D is true.
