Applying the cosine rule is the way to go.Natasha1 said:Homework Statement
In triabgle ABC, AB = 2x cm, AC = x cm, BC = 21 cm and angle BAC = 120 degrees. Calculate the value of x?
Homework Equations
I used the cosine rule here
The Attempt at a Solution
As we have 2 sides and an angle I used the cosine rule - Am I correct?
(2) means squared
b(2) = a(2) + c(2) - 2ac cos B
so
x(2) =21(2) + (2x)(2) - 2.21.2x.c cos B
x(2) =441 + 4x(2) - 84x cos B
3x(2) = 84x cosB - 441
How do I find x from here?
Looks correct (except that the angle should better be called A, not B).Natasha1 said:Thanks everyone, I have found that x(2) = 63 which makes x = 7.94 cm (to 2dp) using the cosine rule
Am I correct?
a(2) = b(2) + c(2) - 2bc cos B
so
21(2) =x(2) + (2x)(2) - 2.x.2x cos B
441 = 5x(2) - 4x(2) cos 120
441 = x(2) (5-4 cos 120)
x(2) = 441 / (5-4cos 120)
x(2) = 63
x = 7.94 cm (to 2dp)
To find the value of x in a triangle ABC, you can use either the Pythagorean Theorem or trigonometric ratios. If you have the lengths of two sides and an angle, you can use the cosine or sine function to solve for x. If you have the lengths of all three sides, you can use the Pythagorean Theorem (a² + b² = c²) to find x.
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In triangle ABC, if you have the lengths of sides a and b, you can use the formula a² + b² = c² to find the length of side c, which is equal to x.
Trigonometric ratios are used to find the missing side or angle in a right triangle. In triangle ABC, you can use the cosine function (cos) to find x if you have the length of one side and the measure of an acute angle. The formula to use is cos(angle) = adjacent/hypotenuse. You can also use the sine function (sin) if you have the length of one side and the measure of an angle that is not adjacent to it.
No, you need to know at least one angle in order to use trigonometric ratios or the Pythagorean Theorem to find the value of x in a triangle ABC. Without any angles, you would need to know the lengths of all three sides to use the Pythagorean Theorem to solve for x.
Yes, you can use the Law of Sines or Law of Cosines to find x in a triangle ABC. The Law of Sines states that the ratio of the length of a side to the sine of its opposite angle is equal for all sides and angles in a triangle. The Law of Cosines can be used when you have the lengths of all three sides and need to find the measure of an angle or the length of a side. Both of these laws involve trigonometric functions and can be used to find the value of x in a triangle ABC.