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likoan [24]
2 years ago
5

I would really appreciate it if someone helped answer these 4 questions. I will rate 5 stars. Thank you (:

Mathematics
1 answer:
ELEN [110]2 years ago
6 0

Answer:

7. 13.6

8. 19.5

9. 6.5

10. 12.6

Step-by-step explanation:

Recall the three main trig functions

Sine = opposite / hypotenuse

Cosine = adjacent / hypotenuse

Tangent = opposite / adjacent

( remember hypotenuse = longest side length , opposite = side length opposite of angle , and adjacent = side length thats not the opposite or hypotenuse )

We will use these to solve each problem

7.

We are given :

  • An angle with a measure of 39 degrees
  • The angles opposite side length
  • The adjacent side as the unknown

When dealing with opposite and adjacent we use tangent

We have tan = opp / adj

==> plug in opp = 11 and adj = x as well as given angle 39

tan(39) = 11/x

==> multiply both sides by x

xtan(39) = 11

divide both sides by tan(39)

x = 11/tan(39)

plugging this into a calculator , we get x = 13.6 ( rounded )

8.

We are given :

  • an angle with a measure of 46 degrees
  • the hypotenuse which has a length of 28
  • and the adjacent as the unknown

When dealing with adjacent and hypotenuse we use cos

We have cos = adj / hyp

==> plug in given angle 46 , adj = x and hyp = 28

cos(46) = x/28

==> multiply both sides by 28

x = 28cos(46)

plugging this into a calculator we get  x = 19.5 ( rounded )

9.

We are given :

  • an angle with a measure of 51 degrees
  • its opposite side length with a length of 8
  • the adjacent side length as the unknown

When dealing with the opposite and adjacent we use tangent

We have tan = opp / adj

==> plug in 51 degrees for angle , opp = 8 and adj = x

tan(51) = 8/x

==> multiply both sides by x

xtan(51) = 8

==> divide both sides by tan(51)

x=8/tan51

plugging this into a calculator we get that x = 6.5 ( rounded )

10.

We are given:

  • an angle with a measure of 24 degrees
  • the hypotenuse which has a length of 31
  • the side length opposite of given angle as the unknown

When dealing with the opposite and hypotenuse we use sine

We have sin = opp / hyp

==> plug in angle as 24 , opp = x and hyp = 31

sin(24) = x / 31

==> multiply both sides by 31

31sin(24) = x

plugging this into a calculator we get that x = 12.6 ( rounded )

And we are done!

Let me know if you have any doubts in the comments ! : )

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