Question

Can someone please help

Answer 1

`\boxed{ \boxed{ \tt{3. \: \: \: \: \underline{ \: 11.85}}}}`

`\boxed{ \boxed{ \tt{ \: 4. \: \: \: \: \: \: \: \underline{13 √(3) \: cm}}}}`

Explanation:

First , A simple way how to remind the three basic trigonometric functions is by reminding the famous word " SOHCAHTOA". We divide the word in three words with three letters.

`\underline{ \underline{ \sf{SOH , \: CAH , \: TOA}}}` :

• The first letter of each word represents the name of the function.
• The second letter represents what's up the ratios sign.
• The third one represents what's at the bottom of the ratio sign.

We write :

• 
  `\sf{sin \: \theta = (opposite)/(hypotenuse) }`
• 
  `\sf{cos \: \theta = (adjacent)/(hypotenuse)}`
• 
  `\sf{tan \: \theta = (opposite)/(adjacent)}`

Now , Let's work on it :

3. Based on the figure ( 3 ) , we know the hypotenuse ( i.e 15 ) & the angle 53° & we have to find the opposite ( x ).

`\sf{ \sin(53) = (opposite)/(hypotenuse) }`

⇾
`\sf{0.79 = (x)/(15)}`

⇾
`\sf{x = 11.85}`

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5. Based on the figure ( 4 ) , we know the adjacent ( i.e 13 cm & the angle 60° & we have to find the opposite ( x ).

`\sf{ \tan(60}) = (opposite)/(adjacent)`

⇾
`\sf{ √(3) = (x)/(13) }`

⇾
`\sf{x = 13 √(3)}` cm

And we're done !

Hope I helped ! ツ

Have a wonderful day / night ! ♡

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