Answer:
[tex] \boxed{ \boxed{ \tt{3. \: \: \: \: \underline{ \: 11.85}}}}[/tex]
[tex] \boxed{ \boxed{ \tt{ \: 4. \: \: \: \: \: \: \: \underline{13 \sqrt{3} \: cm}}}}[/tex]
Step-by-step 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.
[tex] \underline{ \underline{ \sf{SOH , \: CAH , \: TOA}}}[/tex] :
- 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 :
- [tex] \sf{sin \: \theta = \frac{opposite}{hypotenuse} }[/tex]
- [tex] \sf{cos \: \theta = \frac{adjacent}{hypotenuse}} [/tex]
- [tex] \sf{tan \: \theta = \frac{opposite}{adjacent}} [/tex]
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 ).
[tex] \sf{ \sin(53) = \frac{opposite}{hypotenuse} }[/tex]
⇾ [tex] \sf{0.79 = \frac{x}{15}} [/tex]
⇾ [tex] \sf{x = 11.85}[/tex]
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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 ).
[tex] \sf{ \tan(60}) = \frac{opposite}{adjacent} [/tex]
⇾ [tex] \sf{ \sqrt{3} = \frac{x}{13} }[/tex]
⇾ [tex] \sf{x = 13 \sqrt{3}} [/tex] cm
And we're done !
Hope I helped ! ツ
Have a wonderful day / night ! ♡
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