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ctyrector
05.03.2021 •
Mathematics
THIS IS URGENT graph the lines given by this equation y=3-2x (whole numbers only)
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Ответ:
The Radius of circle is 7.15 cm
Step-by-step explanation:
Given as :
A Triangle is inscribed into circle
The center of circle is O
The Diameter of circle = AK = d
The hypotenuse of triangle being the diameter of circle
The Area of triangle = 50 cm²
Let The radius of circle = r cm
The Triangle is right angle at c
So , ∠ACK = 90°
∠CAK = 42°
∠AKC = 180° - (90° + 42°)
So, ∠AKC = 48°
Now, ∵ Area of triangle ACK = 50 cm²
So,
× AC × CK = 50
Or, AC × CK = 50 × 2
i.e , AC × CK = 100 ..........1
From figure
Sin 48° =![\dfrac{AC}{AK}](/tpl/images/0440/7250/61042.png)
Or, 0.74 =![\dfrac{AC}{d}](/tpl/images/0440/7250/8c58a.png)
∴ AC = 0.74 d ..........2
Similarly
Sin 42° =![\dfrac{CK}{AK}](/tpl/images/0440/7250/c39fa.png)
Or, 0.66 =![\dfrac{CK}{d}](/tpl/images/0440/7250/f8a5c.png)
∴ CK = 0.66 d .............3
Putting eq 2 and 3 value into eq 1
i.e AC × CK = 100
Or, 0.74 d × 0.66 d = 100
Or, 0.4884 × d² = 100
∴ d² =![\dfrac{100}{0.4884}](/tpl/images/0440/7250/c93e5.png)
Or, d² = 204.75
Or, d =![\sqrt{204.75}](/tpl/images/0440/7250/9593e.png)
Or, d = 14.30
So, The diameter of circle = d = 14.30 cm
Now, Radius of circle =![\dfrac{\textrm diameter}{2}](/tpl/images/0440/7250/cc96f.png)
Or, r =![\dfrac{\textrm 14.30 cm}{2}](/tpl/images/0440/7250/f0c4b.png)
i.e r = 7.15 cm
So, The Radius of circle = r = 7.15 cm
Hence, The Radius of circle is 7.15 cm Answer