Answer:
[tex]\boxed {\boxed {\sf x \approx 105.3}}[/tex]
Step-by-step explanation:
To solve for x, remember the right triangle trigonometry ratios (soh-cah-toa).
- sinθ= opposite/hypotenuse
- cosθ= adjacent/hypotenuse
- tanθ= opposite/adjacent
If we look at the angle given (θ), then we see that 36 is adjacent or next to the 70° angle. x is the hypotenuse because it is opposite the right angle. So, we have to use cosine (adjacent and hypotenuse).
[tex]cos (\theta)=\frac {adjacent}{hypotenuse}[/tex]
[tex]cos(70)=\frac{36}{x}[/tex]
Cross multiply. (Multiply the first numerator by the second denominator. Then, multiply the first denominator by the second numerator).
[tex]\frac{cos(70)}{1}=\frac{36}{x}[/tex]
[tex]cos(70)*x= 36[/tex]
Since we want to solve for x, we must isolate the variable. Divide both sides by the cosine of 70.
[tex]\frac{cos(70)*x}{cos(70)}=\frac{ 36}{cos(70)}\\x= 105.2569584[/tex]
Round to the nearest tenth. The 5 in the hundredth place tells us to round the 2 to a 3.
[tex]x \approx 105.3[/tex]
x is about 105.3
