if the sin(3x + 10)° = cos(x + 24)°, find x. ...
if the sin(3x + 10)° = cos(x + 24)°, find x. a x = 10 b x = 14 c x = 20 d x = 28
Answer
# Answer:
A. $x = 14$
# Explanation:
## Step1: Use co - function identity
We know that $\sin\alpha=\cos(90^{\circ}-\alpha)$. So, $3x + 10+(x + 24)=90$.
## Step2: Combine like terms
$(3x+x)+(10 + 24)=90$, which simplifies to $4x+34 = 90$.
## Step3: Isolate the variable term
Subtract 34 from both sides: $4x=90 - 34$, so $4x=56$.
## Step4: Solve for x
Divide both sides by 4: $x=\frac{56}{4}=14$.