Explain why a square must be a rectangle but a rectangle does not have to be a square
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.
Answer:
Step-by-step explanation:
What you have here is classic right triangle trig. The height of the tower is the height of a right triangle, and the point 50 feet from the base of the tower is the base of the triangle. The angle of elevation is the base angle that is NOT the right angle. The height is opposite the base angle, while the base is adjacent to the angle, so we need the tangent ratio to find the angle. Here's what we have:
When you are looking for a missing angle, you use the inverse of the angle on your calculator. To do this, hit the 2nd button, then tan, and what you see on your screen is
Enter 200/50 (or 4) and hit "enter" to find the missing angle. It comes out to 75.9 so 76 degrees.