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Given the following 30-60-90 triangle , find the value of x and y Round to the nearest tenth x = 5.2 X = 6 Y = 6 Y = 5.2​

Given the following 30-60-90 triangle , find the value of x and y Round to the nearest-example-1

2 Answers

7 votes

Explanation:

tan30° = Opposite/Adjacent = 3/x.

=> 3/x = √3/3, x = 3√3 = 5.2.

sin30° = Opposite/Hypotenuse = 3/y.

=> 3/y = 1/2, y = 6.

The correct answer is the 1st and 3rd options.

User Anuja Lamahewa
by
8.1k points
8 votes

Answer:


\huge \boxed{ \boxed{ \sf \: x = 5.2 \atop\sf y = 6}}

Explanation:

to understand this

you need to know about:

  • trigonometry
  • PEMDAS

given:


  • \theta = {30}^(o)
  • opp:3

to find:

  • adjacent (x)
  • hypotenuse (y)

tips and formulas:


  • \tan( {30}^(o) ) = ( √(3) )/(3)
  • tan(a)=opp/adj
  • sin(a)=opp/hypo

  • \sin( {30}^(o) ) = (1)/(2)

let's solve:

according to the question


\tan( {30}^(o) ) = (3)/(x)


( √(3) )/(3) = (3)/(x) \\ x√(3) = 9 \\ x = (9)/( √(3) ) \\ x = 3√(3) \\ x = 5.2

according to the question


\sin( {30}^(o) ) = (3)/(y)


(1)/(2) = (3)/(y)


y = 6

User Oli Girling
by
8.5k points

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