Ex 5.5
1 answer:
;
2 × 5 × sin( π / 12 ) = 10 × sin ( π / 12 ) ;
π/12 = ( 180° ) / 12 = 15°.
<span>
But, sin ( π/12 ) </span>
<span>= sin 15° </span>
<span>= sin ( 45° - 30°) </span>
<span>= sin 45°· cos 30° - cos 45°· sin 30° </span>
<span>= (1/√2)·(√3 /2 ) - (1/√2)·(1/2) </span>
<span>= ( √3 - 1 ) / (2√2) = </span>
;
Finally, ( 2.5 ) × ( 2.4 - 1.4 ) = 2.5 cm ;
2 × 5 × sin( π / 12 ) = 10 × sin ( π / 12 ) ;
π/12 = ( 180° ) / 12 = 15°.
<span>
But, sin ( π/12 ) </span>
<span>= sin 15° </span>
<span>= sin ( 45° - 30°) </span>
<span>= sin 45°· cos 30° - cos 45°· sin 30° </span>
<span>= (1/√2)·(√3 /2 ) - (1/√2)·(1/2) </span>
<span>= ( √3 - 1 ) / (2√2) = </span>
Finally, ( 2.5 ) × ( 2.4 - 1.4 ) = 2.5 cm ;
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One of the same-side exterior angles formed by two lines and a transversal is equal to 1/6 of the right angle and is 11 times smaller than the other angle. Then the lines are parallel
<h3><u>Solution:</u></h3>Given that, One of the same-side exterior angles formed by two lines and a transversal is equal to 1/6 of the right angle and is 11 times smaller than the other angle.
We have to prove that the lines are parallel.
If they are parallel, sum of the described angles should be equal to 180 as they are same side exterior angles.
Now, the 1st angle will be 1/6 of right angle is given as:
And now, 15 degrees is 11 times smaller than the other
Then other angle = 11 times of 15 degrees
Now, sum of angles = 15 + 165 = 180 degrees.
As we expected their sum is 180 degrees. So the lines are parallel.
Hence, the given lines are parallel