Use a half-angle identity to find the exact value of sin 3pi/8
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<u>Answer:</u>
A building makes a angle with the ground .The two interior angles are
and
<u>Solution: </u>
Given, a ladder which is against the building wall makes an exterior angle of
And building makes a angle with the ground.
So, altogether it makes a right angle triangle with ladder as hypotenuse and ground as base leg and building as another leg.
Now, we know that, sum of exterior angles and interior angles equals to
Here, in the case of ground and ladder, exterior angle is and interior angle is unknown.
Exterior angle + interior angle = 180
110 + interior angle = 180
Interior angle = 180 – 110
Interior angle =
We have found one of the two interior angles of right angle triangle.
We know that, sum of angles in a triangle is 180 degree
Known Interior angle + unknown interior angle + right angle = 180
70 + unknown interior angle + 90 = 180
Unknown interior angle + 160 = 180
Unknown interior angle = 180 - 160
Unknown interior angle =
Hence the two interior angles are and