trignometry help (1 Viewer)

[Halo189]

any help in these question

6. a point P is 8 cm distant from the centre of a circle of radius length 5 cm. find the length of the major arc between the points of contact of the tangents drawn from pint P to the circle

8. the minute hand of a clock is 20cm long. calculate:
a) the arc length along which the tip of the hand travels in 16 min
b) the shortest distance between the initial and final positions of the tip of the hand

14. a circular metal plate is cut into two segments along a chord equal in length to the radius. what is the ration of the areas of the two segments

thanks

 

[InteGrand]

any help in these question

6. a point P is 8 cm distant from the centre of a circle of radius length 5 cm. find the length of the major arc between the points of contact of the tangents drawn from pint P to the circle

8. the minute hand of a clock is 20cm long. calculate:
a) the arc length along which the tip of the hand travels in 16 min
b) the shortest distance between the initial and final positions of the tip of the hand

14. a circular metal plate is cut into two segments along a chord equal in length to the radius. what is the ration of the areas of the two segments

thanks

Hints/methods:
Q.6
The steps are to draw the diagram, you should have P outside the circle, and join that to the centre O, and to two points where it's tangent on the circle. Finally, join the centre to these two points where the tangents touch the circle (this forms two triangles). Then use the fact that tangent is perpendicular to radii, so the triangles are right-angled. The distance OP is 8 and the radii are 5, so you can use right-angled trig. in these triangles to find the relevant angle, and from this, you can calculate the length of the major arc using arc length formula.

8. a) The angular speed of the minute hand is , so in 16 min., the angle travelled is this angular speed times 16 min. After finding this angle, multiply by the length of the hand to get the distance travelled.

b) For the shortest distance, it's just the length of a chord. This can be found by drawing the triangle with the following vertices: the centre O, the initial point of the hand, and the ending point. Since you calculated the inner angle, you can find the required chord length using the cosine rule.

14. Find the central angle (hint: the relevant triangle is equilateral) and use area of segment formula.

 

[Halo189]

Hints/methods:
Q.6
The steps are to draw the diagram, you should have P outside the circle, and join that to the centre O, and to two points where it's tangent on the circle. Finally, join the centre to these two points where the tangents touch the circle (this forms two triangles). Then use the fact that tangent is perpendicular to radii, so the triangles are right-angled. The distance OP is 8 and the radii are 5, so you can use right-angled trig. in these triangles to find the relevant angle, and from this, you can calculate the length of the major arc using arc length formula.

8. a) The angular speed of the minute hand is , so in 16 min., the angle travelled is this angular speed times 16 min. After finding this angle, multiply by the length of the hand to get the distance travelled.

b) For the shortest distance, it's just the length of a chord. This can be found by drawing the triangle with the following vertices: the centre O, the initial point of the hand, and the ending point. Since you calculated the inner angle, you can find the required chord length using the cosine rule.

14. Find the central angle (hint: the relevant triangle is equilateral) and use area of segment formula.

thanks I got it