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grin007 [14]
3 years ago
14

Find the value of each variable. If you give the decimal value, round to the nearest tenth.

Mathematics
1 answer:
DiKsa [7]3 years ago
7 0

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,

\text{Base}^2+\text{Opposite}^2=\text{Hypotenuse}^2

⇒ 6^2+\text{opposite}^2=12^2

⇒ 36+\text{opposite}^2=144

⇒ \text{opposite}^2=108

⇒ \text{opposite}=6\sqrt3=10.4

⇒ u = 10.4

Hence, u = 10.4 and v = 12.

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