A road curve is to be laid out on a circle. What radius should be used if the track is to change direction by 42^\circ in distance of 44 \text{ m}? (Assume \pi=\frac{22}{7})

Explanation

Using the arc length formula s = r\theta, where \theta is in radians: 44 = r \times 42 \times \frac{\pi}{180}. Substituting \pi = \frac{22}{7}, we get 44 = r \times 42 \times \frac{22}{7 \times 180} \Rightarrow 44 = r \times \frac{132}{180}. Solving for r: r = \frac{44 \times 180}{132} = \frac{180}{3} = 60 \text{ m}.

Related questions on Geometry

• In a triangle ABC, \angle A = 30^\circ, AB = 7 cm and AC = 12 cm. What is the area of the triangle ABC?
• ABC is a triangle right angled at B. D is a point on AC such that BD is perpendicular to AC. If AB = p and BC = \sqrt{3}p, then what is BD...
• The difference between an interior angle and an exterior angle of a regular polygon is 120°. What is the number of sides of the polygon?
• An angle q is exactly one-fourth of its complementary angle. What is the value of angle q?
• The sides of a triangle are 11 cm, 60 cm and 61 cm. What is the area of the triangle formed by joining the mid-points of the sides of the tr...