Math, asked by durgagandharva, 1 month ago

in triangle abc , right angled at b , bc=10cm and angle acb=45 , the length of ac is
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Answers

Answered by MoodyCloud
73

Answer:

Length of AC is 10√2 cm.

Step-by-step explanation:

Given :

  • ABC is right angled triangle at B.
  • Length of BC is 10 cm.
  • ∠ACB is 45°.

To find :

  • Length of AC.

Solution :

Using trigonometry :

 \longrightarrow cos Ѳ = Base/Hypotenuse

• cos 45° = 1/√2

 \longrightarrow 1/√2 = Base/Hypotenuse

 \longrightarrow 1/√2 = BC/AC

 \longrightarrow 1/√2 = 10/AC

• Cross multiple

 \longrightarrow AC = 10 × √2

 \longrightarrow AC = 102

Therefore,

Length of AC is 102 cm.

Attachments:
Answered by ItzShizuka50
59

Answer:

Given :

  • ABC is right angled triangle at B.
  • Length of BC is 10 cm.
  • ∠ACB is 45°

To Find :

  • Length of AC is ?

Solution :

Then using the trigonometry :

\mathsf\blue{⟶  \cos \theta \:  =  base/hypotenuse }

\mathsf\blue {→ \cos 45 \degree \:  = 1/✓2}

\mathsf\blue{⟶ 1/✓2\:  =  base/hypotenuse }

\mathsf\blue{⟶ 1/✓2 = bc/ac }

\mathsf\blue{⟶ 1/✓2 =  \frac{10}{ac} }

✰ Cross multiply

\mathsf\blue{⟶ ac = 10 \times ✓2}

\mathsf\blue{⟶ ac = 10✓2 }

Therefore ,

  • Length of AC is 10✓2 cm.

 \huge\mathsf\purple{. |ItzShizuka50 | .}

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