∆ RST is an equilateral triangle of side 9 cm. If O, Mand N are points on side RS, RT and ST respectivelysuch that OR - 3 cm and ROM = NMO = 90°Find the length of ON.
Answers
Answered by
5
Length of ON = 6 cm where ∆ RST is an equilateral triangle of side 9 cm. M and N are points on side RS, RT and ST respectively such that OR = 3 cm and ∠ROM = ∠NMO = 90°
Step-by-step explanation:
∆ RST is an equilateral triangle
=> ∠R = ∠S = ∠T = 60°
RS = ST = RT = 9 cm
in ΔROM
∠ROM = 90° ∠R = 60°
=> ∠RMO = 30° ( 180° - 90° - 60°)
Sin30 = RO/RM
=> 1/2 = 3 /RM
=> RM = 6 cm
OM² = RM² - RO² = 6² - 3² = 27
MT = RT - RM = 9 - 6 = 3 cm
∠RMO = 30°
∠NMO = 90°
∠RMO + ∠NMO + ∠NMT = 180°
=> ∠NMT = 180° - 30° - 90°
=> ∠NMT = 60°
=> Δ NMT is Equialteral triangle as ∠ T = 60° also
=> NM = MT
=> NM = 3 cm
in ΔNMO
ON² = OM² + NM²
=> ON² = 27 + 3²
=> ON² = 36
=> ON = 6 cm
Length of ON = 6 cm
Learn More:
In as equilateral triangle lmn,the side mn is trisected at o.prove that ...
https://brainly.in/question/8565353
In the given figure ABC is an equilateral triangle and BC is produced ...
https://brainly.in/question/13074151
Similar questions
Social Sciences,
5 months ago
Science,
5 months ago
Math,
5 months ago
Math,
11 months ago
Social Sciences,
1 year ago
History,
1 year ago