Respuesta :
Answer:
In Trigonometry a triangle ABC with the right-angle at B and one angle as 60 degrees, the sides are in the ratio 1:√3:2. Labeling the opposite side of the 60 degrees angle as x, (which is AB), and the adjacent side (BC) as y, from the ratio we get x = 2√3 and y = 12.
Step-by-step explanation:
θ = 60°
Opposite side of θ = 6
Adjacent side of θ = x
Hypotenuse = y
To find:
The value of x and y.
Solution:
Using basic trigonometric ratio formula:
$\tan\theta =\frac{\text{Opposite side of } \theta}{\text{Adjacent side of } \theta}
$\tan60^\circ=(6)/(x)
The value of tan 60° = √3
$√(3) =(6)/(x)
Multiply by x on both sides.
$√(3) * x=(6)/(x) * x
$√(3) * x=6
Divide by √3 on both sides, we get
$(√(3) * x)/(√(3) ) =(6)/(√(3) )
x=2√(3)
Using Pythagoras theorem:
\text{Hypotenuse}^2 = \text{Opposite}^2 + \text{Adjacent}^2
y^2 = 6^2 +({2\sqrt {3}})^2
y^2 = 36 +12
y^2 = 48
Taking square root on both sides, we get
y=4 √(3)
Therefore, the exact values of x and y a=2 √(3), y=4 √(3).
