Question

2
Activity
With the help of the Figure 3.29 above fill in the blanks and complete the proof of the
following theorem.
Theorem : If the acute angles of a right angled triangle have measures 30 and 60 then
the length of the side opposite to 60° angle is x hypotenuse
Proof: In the above theorem we have proved AB AC
AB + BC-
.......... Pythagoras theorem
7 AC+ BC
.: BC² = AC - 1 AC
.: BC=13
.. BC = V3 AC
AC
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Answer 1

Given:

Refer to an attachment for a proper question.

To find:

fill in the blanks and complete the proof of the following theorem.

Solution:

Theorem: If the acute angles of a right-angled triangle have measures 30° and 60° then the length of the side opposite to 60° angle is √3/2 hypotenuse.

Proof: In the above theorem we proved that AB = 1/2 AC

=> AB² + BC² = AC²  --------- Pythagoras theorem

=> 1/4 AC² + BC² = AC² --------- (AB=AC/2)

=> ∴ BC² = AC² - 1/4AC²

=> ∴ BC² = 3/4 AC²

=> ∴ BC = √3/2 AC

Answer 2

Explanation:

hope this help you

this is the activity on page 35