Question

1. In a circle with radius 6.5, an angle measuring 5.5 radians intercepts an arc. Find the length of the arc to the nearest 10th.
2. Two tangents that intersect at P intercept a major arc of 240 degrees on the circle. What is the measure of
3. What are the coordinates of the point on the directed line segment from (−10,10) to (-5,5) that partitions the segment into a ratio of 2 to 3?

Answer 1

Answer:

[1] We know that,

Length of arc(s) = r∅

• 6.5 × 5.5
• 35.75 or 35.8 rounded.

[3] Using section formula,

Let A(-10, 10) and B(- 5, 5) ; m = 2, n = 3 and coordinates of the point be P(x,y)

So,

P(x,y) = {mx2 + nx1/m + n},{my2 + ny1/m + n}

• {2 × - 5 + 3 × - 10/5},{2 × 5 + 3 × 10/5}
• {- 10 + - 30/5},{10 + 30/5}
• {- 40/5},{40/5}
• {- 8, 8}

Hence, Required coordinates are (- 8,8).