To solve such problems we need to know about Trigonometry.
Trigonometric functions
[tex]Sin \theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]
[tex]Cos \theta=\dfrac{Base}{Hypotenuse}[/tex]
[tex]Tan \theta=\dfrac{Perpendicular}{Base}[/tex]
where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.
The value of x is 5√3.
Explanation
Given to us,
- the base for the triangle, AB = 5 units,
- Hypotenuse for the triangle, BC = 10 units,
- ∠B = 60°,
Solution
The question can be solved in two ways,
1. Using the Pythagoras theorem,
According to Pythagoras theorem,
[tex]\rm{(Hypotenuse)^2=(Perpendicular)^2+(Base)^2}[/tex]
substituting the values,
[tex](10^2)=(x^2)+(5^2)\\100 = x^2 +25\\x^2 = 75\\x = \sqrt{75}\\x =5\sqrt3[/tex]
2. using the trigonometric function for ∠B,
for ∠B in ΔABC,
[tex]\rm{tangent(B)=\dfrac{Perpendicular}{Base}}[/tex]
substituting the values,
[tex]\bold{tangent(60^o)=\dfrac{x}{5}}[/tex]
we know that value of tan(60°) is √3,
[tex]\rm tangent(60^o)=\dfrac{x}{5}\\ \sqrt{3}= \dfrac{x}{5}\\x = \sqrt{3}\times 5\\x=5\sqrt3[/tex]
Hence, the value of x is 5√3.
Learn more about Trigonometry:
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