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I need help with this practice problem solving from my ACT prep guide Am I correct ?

I need help with this practice problem solving from my ACT prep guide Am I correct-example-1
User Clotilde
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1 Answer

6 votes

Lets use # to represent tetha

B to represent beta

Given:

cos # = - root2/3

tan B = 4/3

we are to find sin (# + B)

cos # = - root2/3, which shows that # is in the second or third quadrant.

Adj = root 2, hyp = 3

Opp^2 = 3^2 - root 2^2

Opp^2 = 9 - 2

Opp = root 7

Therefore, sin # = root 7/3

Tan B = 4/3

Opp = 4, Adj = 3

Hyp^2 = 4^2 + 3^2

Hyp^2 = 25

Hyp = 5

Sin B = 4/5

Cos B = 3/5

Sin(# + B) = sin#cosB + sinBcos#

Sin(# + B) = root7/3 x 3/5 + 4/5 x -root 2/3

Sin(# + B) = root 7/5 - 4root 2/15

User FeeFiFoFum
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