Answer:
7. 13.6
8. 19.5
9. 6.5
10. 12.6
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 ! : )