If you look closely the area where 3x is congruent to the other side of the 90 degree angle with one part as 0.5x + 34

So
3x + 0.5x + 34= 90

x will be 16

So plug it in

0.5(16) + 34= 42 degrees

And

3(16)= 48 degrees

That left half of the circle is 180 degrees and since we know the angle 3x is 48 degrees we subtract it from 180 to get angle AE

180-48

132 degrees is your answer

7 0

3 years ago

Given that sin theta = 1/4, 0→theta→π/2, what . what is the exact value of cos 8?

natali 33 [55]

<h3>Answer: Choice B $\frac{\sqrt{15}}{4}$ </h3>

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Work Shown:

Angle theta is between 0 and pi/2, so this angle is in quadrant Q1.

Square both sides of the given equation

$\sin \theta = \frac{1}{4}\\\\\sin^2 \theta = \left(\frac{1}{4}\right)^2\\\\\sin^2 \theta = \frac{1}{16}$

Then use the pythagorean trig identity to get

$\sin^2 \theta + \cos^2 \theta = 1\\\\\cos^2 \theta = 1-\sin^2 \theta\\\\\cos \theta = \sqrt{1-\sin^2 \theta} \ \ \ \text{cosine is positive in Q1}\\\\\cos \theta = \sqrt{1-\frac{1}{16}}\\\\\cos \theta = \sqrt{\frac{16}{16}-\frac{1}{16}}\\\\\cos \theta = \sqrt{\frac{16-1}{16}}\\\\\cos \theta = \sqrt{\frac{15}{16}}\\\\\cos \theta = \frac{\sqrt{15}}{\sqrt{16}}\\\\\cos \theta = \frac{\sqrt{15}}{4}\\\\$

3 0

3 years ago