Answer:
x = 60°
Step-by-step explanation:
Trigonometric ratios
[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]
where:
- [tex]\theta[/tex] is the angle
- O is the side opposite the angle
- A is the side adjacent the angle
- H is the hypotenuse (the side opposite the right angle)
As we have been given the hypotenuse and the side adjacent the angle, we can use the cosine trig ratio.
Given:
- [tex]\theta[/tex] = x
- A = 10
- H = 20
Substitute the given values into the cosine trig ratio and solve for x:
[tex]\implies \sf \cos(x^{\circ})=\dfrac{10}{20}[/tex]
[tex]\implies \sf \cos(x^{\circ})=\dfrac{1}{2}[/tex]
[tex]\implies \sf x=\cos^{-1} \left(\dfrac{1}{2}\right)[/tex]
[tex]\implies \sf x=60^{\circ}[/tex]
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