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The isosceles trapezoid is part of an isosceles triangle with a 32 degrees vertex anglewhat is the measure of an acute base angle of the trapezoid?
In an isosceles triangle with a vertex angle of 32 degrees, the base angles are each equal to ( \frac{180^\circ - 32^\circ}{2} = 74^\circ ). Since the isosceles trapezoid is formed from this triangle, the acute base angles of the trapezoid are also equal to the base angles of the triangle. Therefore, the measure of an acute base angle of the trapezoid is 74 degrees.
How many degrees can a decagon can rotate onto itself?
A regular decagon can rotate onto itself at angles that are multiples of ( \frac{360^\circ}{10} ), which is ( 36^\circ ). This means it can rotate by ( 0^\circ ), ( 36^\circ ), ( 72^\circ ), ( 108^\circ ), ( 144^\circ ), ( 180^\circ ), ( 216^\circ ), ( 252^\circ ), ( 288^\circ ), and ( 324^\circ ). In total, there are 10 distinct angles (including ( 0^\circ )) at which the decagon can map onto itself.
What is Given that the measure of and Angle's is 132 and deg and the measure of and angy is 55 and deg find the measure of and angz.?
To find the measure of angle ( \text{angz} ), you can use the fact that the sum of the angles in a triangle is 180 degrees. Given that ( \text{angx} = 132^\circ ) and ( \text{angy} = 55^\circ ), you can calculate ( \text{angz} ) as follows: [ \text{angz} = 180^\circ - \text{angx} - \text{angy} = 180^\circ - 132^\circ - 55^\circ = -7^\circ ] Since a negative angle doesn't make sense in this context, please check the angle values provided.
What is the measure of each angle in a regular polygon with 3 sides?
In a regular polygon with 3 sides, which is a triangle, each angle measures 60 degrees. This is calculated using the formula for the interior angle of a regular polygon, which is ((n-2) \times 180^\circ / n), where (n) is the number of sides. For a triangle, (n = 3), so the calculation is ((3-2) \times 180^\circ / 3 = 60^\circ). Thus, all three angles in an equilateral triangle are equal to 60 degrees.
What is value of tan15' tan195'?
To find the value of (\tan(15^\circ) \tan(195^\circ)), we can use the identity (\tan(195^\circ) = \tan(15^\circ + 180^\circ) = \tan(15^\circ)). Thus, (\tan(195^\circ) = \tan(15^\circ)). Consequently, (\tan(15^\circ) \tan(195^\circ) = \tan(15^\circ) \tan(15^\circ) = \tan^2(15^\circ)). The exact value of (\tan^2(15^\circ)) can be computed, but it is important to note that it will yield a positive value.
What is the value of cos2 67-sin2 23?
To find the value of ( \cos^2 67^\circ - \sin^2 23^\circ ), we can use the identity ( \cos^2 \theta = 1 - \sin^2 \theta ). Since ( \sin 23^\circ = \cos 67^\circ ) (because ( 23^\circ + 67^\circ = 90^\circ )), we have ( \sin^2 23^\circ = \cos^2 67^\circ ). Thus, ( \cos^2 67^\circ - \sin^2 23^\circ = \cos^2 67^\circ - \cos^2 67^\circ = 0 ). Therefore, the value is ( 0 ).
What is the exact value of sin 165?
The exact value of (\sin 165^\circ) can be calculated using the sine subtraction formula. Since (165^\circ = 180^\circ - 15^\circ), we have: [ \sin 165^\circ = \sin(180^\circ - 15^\circ) = \sin 15^\circ ] The value of (\sin 15^\circ) can be derived from the formula (\sin(45^\circ - 30^\circ)), which gives: [ \sin 15^\circ = \sin 45^\circ \cos 30^\circ - \cos 45^\circ \sin 30^\circ = \frac{\sqrt{2}}{2} \cdot \frac{\sqrt{3}}{2} - \frac{\sqrt{2}}{2} \cdot \frac{1}{2} = \frac{\sqrt{6} - \sqrt{2}}{4} ] Thus, (\sin 165^\circ = \frac{\sqrt{6} - \sqrt{2}}{4}).
What is the cofunction of cos 70?
The cofunction of cosine is sine. Therefore, the cofunction of (\cos 70^\circ) is (\sin(90^\circ - 70^\circ)), which simplifies to (\sin 20^\circ). Thus, (\cos 70^\circ = \sin 20^\circ).
What is Cos 15?
The cosine of 15 degrees can be calculated using the cosine subtraction formula: ( \cos(15^\circ) = \cos(45^\circ - 30^\circ) ). This gives us ( \cos(15^\circ) = \cos 45^\circ \cos 30^\circ + \sin 45^\circ \sin 30^\circ ). Plugging in the known values, ( \cos 45^\circ = \frac{\sqrt{2}}{2} ), ( \cos 30^\circ = \frac{\sqrt{3}}{2} ), ( \sin 45^\circ = \frac{\sqrt{2}}{2} ), and ( \sin 30^\circ = \frac{1}{2} ), we find that ( \cos 15^\circ = \frac{\sqrt{6} + \sqrt{2}}{4} ).
What does the prefix circ mean?
The prefix is actually "circ-" means "around."
What is the exact value of tan 195?
The exact value of (\tan 195^\circ) can be found using the tangent addition formula. Since (195^\circ) is in the third quadrant, where tangent is positive, we can express it as (\tan(180^\circ + 15^\circ)). This gives us (\tan 195^\circ = \tan 15^\circ), which is (\frac{\sin 15^\circ}{\cos 15^\circ}). Using the known values, (\tan 15^\circ = 2 - \sqrt{3}). Therefore, (\tan 195^\circ = 2 - \sqrt{3}).
What is 19sin(50) divided by sin(40)?
To find the value of ( \frac{19 \sin(50^\circ)}{\sin(40^\circ)} ), we can use the sine function values. Using the sine of complementary angles, ( \sin(50^\circ) = \cos(40^\circ) ). Therefore, ( \frac{19 \sin(50^\circ)}{\sin(40^\circ)} = \frac{19 \cos(40^\circ)}{\sin(40^\circ)} = 19 \cot(40^\circ) ). For an exact numerical value, you can compute ( 19 \cot(40^\circ) ) using a calculator.
