If the angles are in the ratio 1:5:6, then find the ratio of its sides.
using cosine rule
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Answer:
Some approaches I've brainstormed are:
1)Using sine=opposite/hypotenuse and cosine=adjacent/hypotenuse (I would have no clue how to continue this)
2)Find an equation involving the ratios and sine and use cosθ=sin(90−θ) (angles are in degree units)
3)Find an equation from the sine rule and substitute the cosine rule (?)
Sorry, I don't know how to format this properly!
trigonometry ratio
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edited Jun 16 '17 at 2:10
Ananth Kamath
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asked Jun 16 '17 at 2:00
SMLW
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2 Answers
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Well, it would be 3), sort of. Let's say the angles are α,β,γ in the order as they appear in the ratio, i.e. sinα:sinβ:sinγ=5:6:7, and a,b,c the sides opposite those angles. Then, the cosine rule says (one out of three, you can work the others out yourself, I'm confident) c2=a2+b2−2abcosγ, so
cosγ=a2+b2−c22ab=12(ab+ba−ca⋅cb).
Applying the sine rule, this becomes
cosγ=12(sinαsinβ+sinβsinα−sinγsinα⋅sinγsinβ)=12(56+65−75⋅76)=15.
Calculating those fractions in all three cases is a simple exercise, I hope, and then, you'll have their ratios, too.
hope it helps you and if helpful then mark as brainlist and vote for it....
Answer:
angles = 1*180/12 = 15° , 5*15 = 75° and 90°
ratio of sides = 1:(√3+2):(√1²+(√3+2)²)
= 1:(√3+2):2(√2+√3) (Ans)