Sumali sa IDNStudy.com at makakuha ng mga sagot sa iyong mga tanong. Makakuha ng impormasyon mula sa aming mga eksperto, na nagbibigay ng maaasahang sagot sa lahat ng iyong mga tanong.
Sagot :
There are two ways to find the radius of circumscribing circle of a triangle (triangle inside the circle and whose three vertices are on the circle).
Choose one that you can easily remember:
Method A:
1.) Find the semi-perimeter (s) of the triangle, where a, b, and c are the sides
of the triangle:
s = (a + b+ c) ÷ 2
2.) Solve for the radius (r) given the semi-perimeter (s) of the triangle, and the
the sides a, b, and c:
r = [tex] \frac{abc}{4 \sqrt{s(s-a)(s-b)(s-c)} } [/tex]
Solution using Method A:
a = 80 cm; b = 100 cm; c = 140 cm
Find the triangle's semi-perimeter: (half of the triangle's perimeter)
s = (80 + 100 + 140) ÷ 2
s = 320 cm ÷ 2
s = 160 cm
Solve for radius given the semi-perimeter (160 cm) and sides a, b, c:
r = (abc) ÷ [tex]4 \sqrt{s(s-a)(s-b)(s-c)} [/tex]
r = [tex] \frac{(80cm)(100cm)(140cm)}{4 \sqrt{140cm(160cm-80cm)(160cm-100cm)(160cm-140cm)} } [/tex]
r = [tex] \frac{1,120,000cm ^{3} }{4 \sqrt{(160cm)(80cm)(60cm)(20cm)} } [/tex]
r = [tex] \frac{1,120,000cm ^{3} }{4 \sqrt{15,360,000cm ^{4} } } [/tex]
r =[tex] \frac{1,120,000cm ^{3} }{4 (3,919.18cm ^{2}) } [/tex]
r = [tex] \frac{1,120,000cm ^{3} }{15,676.72cm ^{2} } [/tex]
r ≈ 71.44 cm
ANSWER: The radius of circumscribing circle is 71.44 cm.
Method B:
r = [tex] \frac{abc}{ \sqrt{(a+b+c)(b+c-a)(c+a-b)(a+b-a)} } [/tex]
Substitute the given measurements of sides a, b and, c, then evaluate.
The result is the same.
Choose one that you can easily remember:
Method A:
1.) Find the semi-perimeter (s) of the triangle, where a, b, and c are the sides
of the triangle:
s = (a + b+ c) ÷ 2
2.) Solve for the radius (r) given the semi-perimeter (s) of the triangle, and the
the sides a, b, and c:
r = [tex] \frac{abc}{4 \sqrt{s(s-a)(s-b)(s-c)} } [/tex]
Solution using Method A:
a = 80 cm; b = 100 cm; c = 140 cm
Find the triangle's semi-perimeter: (half of the triangle's perimeter)
s = (80 + 100 + 140) ÷ 2
s = 320 cm ÷ 2
s = 160 cm
Solve for radius given the semi-perimeter (160 cm) and sides a, b, c:
r = (abc) ÷ [tex]4 \sqrt{s(s-a)(s-b)(s-c)} [/tex]
r = [tex] \frac{(80cm)(100cm)(140cm)}{4 \sqrt{140cm(160cm-80cm)(160cm-100cm)(160cm-140cm)} } [/tex]
r = [tex] \frac{1,120,000cm ^{3} }{4 \sqrt{(160cm)(80cm)(60cm)(20cm)} } [/tex]
r = [tex] \frac{1,120,000cm ^{3} }{4 \sqrt{15,360,000cm ^{4} } } [/tex]
r =[tex] \frac{1,120,000cm ^{3} }{4 (3,919.18cm ^{2}) } [/tex]
r = [tex] \frac{1,120,000cm ^{3} }{15,676.72cm ^{2} } [/tex]
r ≈ 71.44 cm
ANSWER: The radius of circumscribing circle is 71.44 cm.
Method B:
r = [tex] \frac{abc}{ \sqrt{(a+b+c)(b+c-a)(c+a-b)(a+b-a)} } [/tex]
Substitute the given measurements of sides a, b and, c, then evaluate.
The result is the same.
Salamat sa iyong pakikilahok. Patuloy na magbahagi ng iyong mga ideya at kasagutan. Sama-sama tayong magpapaunlad ng isang komunidad ng karunungan at pagkatuto. Gawin mong pangunahing mapagkukunan ang IDNStudy.com para sa maasahang mga sagot. Nandito kami para sa iyo.
