Question

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​

Answer 1

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.

Answer 2

`\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`