An equilateral triangle has a side length measure that is represented by 2x+4. What is the perimeter of the triangle? And how wo
2 answers:
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Answer:
30°
Step-by-step explanation:
Call the other end of the chord point B and the center of the circle point O. Then triangle AOB is an equilateral triangle, since OA = OB = AB.
Angle OAB is the internal angle of that triangle, so is 60°. Since OA is perpendicular to the tangent line (makes an angle of 90°), The angle between the tangent line and the chord must be ...
90° - 60° = 30°
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The other way you know this is that central angle AOB is 60°, and the tangent-to-chord angle is half that, or 30°.
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One way to remember the angle relationship between a tangent line and a chord is this:
Consider a point C on long arc AB. The measure of inscribed angle ACB is half the measure of central angle AOB, no matter where C is on the circle. (If C happens to be on the short arc AB, then central angle AOB is a reflex angle, but the relationship still holds.) Consider what happens when C approaches A. The angle at vertex C is still the same: 1/2 the measure of central angle AOB. This remains true even in the limit when points A and C become coincident and line AC is a tangent at point A.
The distance from the sun is option 2 5.59 astronomical units.
Step-by-step explanation:
Step 1; To solve the question we need two variables. P which represents the number of years a planet takes to complete a revolution around the Sun. This is given as 13.2 years in the question so P = 13.2 years. The other variable is the distance between the planet and the sun in astronomical units. We need to determine the value of this using the given equation.
Step 2; So we have to calculate the value of 'a' in Kepler's equation. But the exponential power is on the variable we need to find so we multiply both the sides by an exponential power of
to be able to calculate 'a'.
P = ,
=
,
= a,
= a = 5.58533 astronomical units.
Rounding it over to nearest hundredth we get 5.59 astronomical units.