In triangle ABC, side AB = 7, side BC = 8, and angle ABC = 60 degrees. What is the length of side AC?
Answer and explanation
Correct answer: A. sqrt(57)
- Step 1: Apply the law of cosines: AC^2 = AB^2 + BC^2 - 2ABBC*cos(60 degrees).
- Step 2: Substitute values: AC^2 = 7^2 + 8^2 - 2 7 8 * 0.5.
- Step 3: AC^2 = 49 + 64 - 56 = 113 - 56 = 57.
- Step 4: AC = sqrt(57).
Answer
sqrt(57).
Why not the others: sqrt(97) computes 113 - 16; sqrt(113) forgets the cosine term entirely (hypotenuse formula); sqrt(65) computes 49 + 64 - 48.
Practise more Plane Geometry, Coordinate Systems and Data Interpretation.
Free questions with an explanation for every one, and full timed Psychometric Entrance Test (PET Israel) mock tests.
More Plane Geometry, Coordinate Systems and Data Interpretation questions
- In a right triangle ABC with hypotenuse AC = 10, angle BAC = 30 degrees. What is the area of triangle ABC?
- A circle of radius r is inscribed in an equilateral triangle of side length 12. What is the area of the circle?
- A square is inscribed in a right isosceles triangle such that one side of the square lies on the hypotenuse. If the hypotenuse has length 12…
- A sector of a circle with central angle 120 degrees has an arc length of 8*pi cm. What is the area of the sector?
- A regular hexagon has perimeter 36 cm. What is its total area?
- Two chords AB and CD intersect inside a circle at point P. If AP = 4, PB = 9, and CP = 3, what is the length of chord CD?