Math, asked by bowserhunter04, 2 days ago

(PLEASE HELP) special right triangles image below

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Answers

Answered by YourHelperAdi
55

To Find :

The value of x and y from the figure .

Given Figure :

Given figure is a triangle , which is made up of two right triangles.

The smaller right triangle has x as its hieght

The bigger right triangle has y as its hypotenuse

Given :

  • hypotenuse of smaller triangle = 122 cm
  • Angle opposite to x in smaller triangle = 45°
  • Angle opposite to x in bigger triangle = 30°
  • hypotenuse of bigger triangle = y

We know that :

 \tt{ \bull \: sin \theta =  \frac{side \: opposite \: to  \:  \theta}{hypotenuse} }

 \tt{ \bull \: sin45 \degree =  \frac{1}{ \sqrt{2} } }

 \tt{ \bull \:cosec \theta =  \frac{hypotenuse}{side \: opposite \: to \:  \theta}}

 \tt{ \bull \: cosec30 \degree = 2}

Solution :

In the smaller triangle,

hypotenuse = 122 cm

Side opposite to Theta = x

Theta = 45°

 \tt{ \implies \: sin \theta =  \frac{side \: opposite \: to \: \theta}{hypotenuse} }

 \implies \tt{sin45 \degree =  \frac{x}{12 \sqrt{2} } }

 \tt{putting \: the \: value \: of \: sin 45 \degree}

 \implies \tt{ \frac{1}{ \sqrt{2}  } =  \frac{x}{12 \sqrt{2} }  }

 \implies \tt{x =  \frac{12 \sqrt{2} }{ \sqrt{2} } }

 \implies \red{ \underline{  \boxed{\tt{x = 12 \: cm}}}}

In the bigger triangle,

hypotenuse = y

side opposite to Theta = x = 12 cm

Theta = 30°

 \implies \tt{cosec \theta =  \frac{hypotenuse}{side \: opposite \: to \: \theta} }

 \tt{ \implies \: cosec30 \degree =  \frac{y}{12} }

 \tt{putting \: the \: value \: of \: cosec 30 \degree}

 \implies \tt{2 =  \frac{y}{12} }

 \implies \tt{y = 12 \times 2}

 \implies \green{ \underline{ \boxed{ \tt{y = 24 \: cm}}}}

so, The values of x and y are :

  • x = 12 cm
  • y = 24 cm

hence, the correct option is a)

________________________________

Additional information:

The valued of "sin theta" and "cosec theta" are just reciprocal of each other,

here, theta 0

 \tt{ \bull \: sin0 \degree = 0}

 \tt{ \bull \: sin30\degree =   \frac{1}{2} }

 \tt{ \bull  \: sin45\degree =  \frac{1}{ \sqrt{2} } }

 \tt{ \bull \: sin60\degree =  \frac{ \sqrt{3} }{2} }

 \tt{ \bull \: sin90\degree = 1}

The value of cosec theta is reciprocal just when , theta0

 \tt{ \bull \: cosec0\degree =  \infin}

 \tt{ \bull \: cosec30\degree = 2}

 \tt{ \bull \: cosec45\degree =   \sqrt{2} }

 \tt{ \bull \: cosec60 \degree =  \frac{2}{ \sqrt{3} } }

 \tt{ \bull \: cosec90\degree = 1}

Answered by choudhryhello
32

Answer:

Step-by-step explanation:

To Find :

The value of x and y from the figure .

Given Figure :

Given figure is a triangle , which is made up of two right triangles.

The smaller right triangle has x as its hieght

The bigger right triangle has y as its hypotenuse

Given :

hypotenuse of smaller triangle = 12√2 cm

Angle opposite to x in smaller triangle = 45°

Angle opposite to x in bigger triangle = 30°

hypotenuse of bigger triangle = y

We know that :

Solution :

In the smaller triangle,

hypotenuse = 12√2 cm

Side opposite to Theta = x

Theta = 45°

In the bigger triangle,

hypotenuse = y

side opposite to Theta = x = 12 cm

Theta = 30°

so, The values of x and y are :

x = 12 cm

y = 24 cm

hence, the correct option is a)

________________________________

Additional information:

The valued of "sin theta" and "cosec theta" are just reciprocal of each other,

here, theta ≠ 0

The value of cosec theta is reciprocal just when , theta≠0

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