In triangle ABC, a=7.8, b=4.2, c=3.9. Find B
a. 15.1°
b. 148.7°
c. 78.9°
d. 16.2 °
It is D, right?
Looks like a situation for the law of cosines.
b^2 = a^2 + c^2 - 2ac cos B
17.64 = 60.84 + 15.21 - 60.84 cos B
cos B = 0.9601
B = 16.2 degrees
To find angle B in triangle ABC, you can use the Law of Cosines, which relates the lengths of the sides of a triangle to the cosine of one of its angles.
The Law of Cosines states that: c^2 = a^2 + b^2 - 2ab * cos(C), where c is the side opposite angle C.
In this case, we have side c = 3.9 (opposite angle C), side a = 7.8, and side b = 4.2.
So, plugging in the values into the Law of Cosines equation, we get:
3.9^2 = 7.8^2 + 4.2^2 - 2 * 7.8 * 4.2 * cos(C)
Simplifying the equation, we get:
15.21 = 60.84 + 17.64 - 65.52 * cos(C)
Rearranging the equation, we have:
15.21 - 78.48 = -65.52 * cos(C)
-63.27 = -65.52 * cos(C)
Dividing both sides by -65.52, we have:
cos(C) ≈ 0.965
To find angle C, we can use the inverse cosine function (cos⁻¹) on our calculator or using trigonometric tables.
cos⁻¹(0.965) ≈ 15.1°
Therefore, the answer is A. B ≈ 15.1°.