Question

Find the missing variables

Answer 1

Explanation:

`\underline{ \underline{ \text{Given}}} :`

• Hypotenuse ( h ) = 8√2
• Perpendicular ( p ) = u
• Base ( b ) = v
• 
  `\tt{ \theta = 45 \degree}`

`\underline{ \underline {\text{To \: find}}} :`

• Value of u & v

`\underline{ \underline{ \text{Solution}}}\:` :

`\tt{sin \: \theta = (p)/(h)}`

⟶
`\tt{ \sin(45 \degree) = (u)/(8 √(2) ) }`

⟶
`\tt{ (1)/( √(2) ) = (u)/(8 √(2)) }`

⟶
`\tt{ √(2 \: ) u = 8 √(2)}`

⟶
`\tt{u = (8 √(2) )/( √(2)) }`

⟶
`\tt{u = 8}`

Again ,

`\tt{tan \: \theta = (p)/(b)}`

⟶
`\tt{ \tan(45 \degree) = (8)/(v)}`

⟶
`\tt{1 = (8)/(v)}`

⟶
`\tt{v = 8}`

`\red{ \underline{ \boxed{ \boxed{ \text{Our \: final \: answer : \boxed{ \tt{u = 8 \: and \: v = 8}}}}}}}`

Hope I helped ! ♡

Have a wonderful day / night ! ツ

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Answer 2

Solution,

tan45 =
`(u)/(v)`

or, 1 =
`(u)/(v)`

or, v = u

Now,

Using Pythagoras Theorem,

`(8√(2))^(2) = u^(2) +v^(2)\\or, 128 = u^(2) +u^(2)\\or, 128 = 2u^(2)\\or, u^(2) = 64\\\\or, u = 8cm = v`