ABC is a triangle right angled at B with AC=2BC. If \angle A=x, then what is \angle C equal to?
- A. \frac{x}{2}
- B. 2x ✓
- C. \sqrt{2}x
- D. \sqrt{3}x
Correct Answer: B. 2x
Explanation
In right-angled triangle ABC, \sin A = \frac{BC}{AC} = \frac{BC}{2BC} = \frac{1}{2}. Thus, \angle A = x = 30^\circ. The remaining angle \angle C = 90^\circ - 30^\circ = 60^\circ. Since x = 30^\circ, \angle C = 2x.
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...