Question

Theorem: If the acute angles of a right angled triangle have measures 30° and 60 , then
the length of the side opposite to 30° angle is half the length of the hypotenuse.
(Fill in the blanks and complete the proof .)​

Answer 1

we have to prove : If the acute angles of a right angled triangle have measures 30° and 60° , then

the length of the side opposite to 30° angle is half the length of the hypotenuse.

proof : let a, b and c are the side lengths of the opposite to 30°, 60° and 90° respectively.

using sine rule,

a/sin30° = b/sin60° = c/sin90°

⇒a/(1/2) = b/(√3/2) = c/(1)

⇒a/0.5 = b/0.866 = c/1

i.e., a/0.5 = c/1 ⇒a = 0.5 c

⇒a = 1/2 c

Therefore it is clear that length of the side opposite to 30° angle is half of the length of hypotenuse.

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Answer 2

Given : In △ ABC

M∠ = 90°

To Prove : BC = √3/2 AC

Proof : In △ ABC