At a local park there is a large compass painted on the sidewalk. Blaine starts at due north and walks 150° in a clockwise direc
tion. Using the unit circle, find the sine value of his current position.
A) negative square root of 3 over 2.
B) square root 2 over 2.
C) one half.
D) negative one half.
A) negative square root of 3 over 2.
B) square root 2 over 2.
C) one half.
D) negative one half.
1 answer:
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In this attached picture according to the conditions of the problem we have an isosceles trapezoid and since we know that legs are equal (AD=BC=5 cm), we have to calculate bases and height in order to find the area. Working with the triangle BCD, we apply Pythagoras theorem and find that CD = = 10 cm. Since BDC is a right triangle, applying theorem for the area of triangles, we find that
and BF=
. Since ABCD is an isosceles trapezoid, triangles ADE and BFC are congruent with Angle Side Angle theorem. Then, DE=FC and with the help of Pythagoras theorem, DE=FC=2.5 cm. Then, AB=EF=5 cm and the area of the trapezoid is
