u = 10.4 and v = 12
Solution:
In the given 2 sides of a triangle are 60°, 60°.
Sum of all the angles of a triangle = 180°
60° + 60° + third angle = 180°
⇒ third angle = 180° – 60° – 60°
⇒ third angle = 60°
All angles are equal, therefore the given triangle is an equilateral triangle.
⇒ All sides are equal in length.
⇒ v = 12
The line drawn from the top angle divides the triangle into two equal parts
and the line is perpendicular.
12 ÷ 2 = 6
Using Pythagoras theorem,
[tex]\text{Base}^2+\text{Opposite}^2=\text{Hypotenuse}^2[/tex]
⇒ [tex]6^2+\text{opposite}^2=12^2[/tex]
⇒ [tex]36+\text{opposite}^2=144[/tex]
⇒ [tex]\text{opposite}^2=108[/tex]
⇒ [tex]\text{opposite}=6\sqrt3=10.4[/tex]
⇒ u = 10.4
Hence, u = 10.4 and v = 12.
