The length of the missing sides of the triangles are as follows:
DE = 12, DF = 12√2, FG = 12√2 and DG = 24.
What is the Pythagoras theorem?
The Pythagoras theorem states that the square of the longest side must be equal to the sum of the square of the other two sides in a right-angle triangle.
ΔDEF is a right angle triangle. We can use Pythagoras theorem to find the sides of the triangle.
c² = a² + b²
where
c = hypotenuse side = DE = 12
a and b are the other 2 legs
lets use trigonometric ratio to find DE ,
tan 45 = Perpendicular / adjacent
tan 45 = DE / 12
DE = 1 × 12
DE = 12
12² + 12² = DF²
DF² = 288
DF = √288 = 12√2
Triangle DFG
DFG is a right angle triangle too. Therefore,
Using trigonometric ratio,
tan 45 = DF / FG
1 = DF / FG
FG = 12√2
(12√2)² + (12√2)²= DG²
DG = 24
Learn more about trigonometric ratios on:
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