Find the value of each variable.

see explanation

Step-by-step explanation:

Using the exact values of the trigonometric ratios

sin60° = , cos60° =

sin45° = cos45° =

Using the sine ratio on the right triangle on the left

sin60° = = =

Cross- multiply

2a = 4 × = 12 ( divide both sides by 2 )

a = 6

Using the cosine ratio on the same right triangle

cos60° = = =

Cross- multiply

2c = 4 ( divide both sides by 2 )

c = 2

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Using the sine/cosine ratios on the right triangle on the right

sin45° = = =

Cross- multiply

b = 6

cos45° = = =

Cross- multiply

d = 6 ( divide both sides by )

d = 6

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a = 6, b = 6, c = 2, d = 6

option 1

data plot with   3 dots over 33, 1 dot over 34, 2 dots over 35, no dot over 36, 1 dot over 37, 2 dots over 38, 4 dots over 39, and 2 dot over 40.