Answer:
[tex]\boxed {\boxed {\sf x \approx 49}}[/tex]
Step-by-step explanation:
This is a right triangle, so the trigonometric ratios can be used.
- sinθ= opposite/hypotenuse
- cosθ= adjacent/hypotenuse
- tanθ= opposite/adjacent
Examine the sides. We see that 10 is the hypotenuse (it is opposite the right angle). 6.5 is adjacent to x. So, we should use cosine.
[tex]cos (\theta)= \frac {adjacent}{hypotenuse}[/tex]
[tex]cos (x)= \frac {6.5}{10}[/tex]
Since we are solving for an angle, we use the inverse trigonometric function.
Move the cosine to the other side and use the inverse.
[tex]x= cos^{-1} (\frac{6.5}{10})[/tex]
Put the right side into a calculator.
[tex]x=49.45839813[/tex]
Round to the nearest whole number. The 4 in the tenth place tells us to leave the number as is.
[tex]x \approx 49[/tex]
x is approximately 49 degrees.
