In triangle ABC, side a=7, b=6, and c=8. Find the measure of angle B to the nearest degree.
use the cosine law in this form
6^2 = 7^2 + 8^2 - 2(7)(8)cos B
let me know if you don't get angle B = 47°
To find the measure of angle B in triangle ABC, we can use the Law of Cosines. The Law of Cosines states that for any triangle with sides a, b, and c, and angle C opposite side c, the following equation holds:
c^2 = a^2 + b^2 - 2ab*cos(C)
In our case, we have sides a=7, b=6, and c=8. Let's substitute these values into the equation and solve for cos(C):
8^2 = 7^2 + 6^2 - 2*7*6*cos(C)
64 = 49 + 36 - 84*cos(C)
64 = 85 - 84*cos(C)
84*cos(C) = 85 - 64
84*cos(C) = 21
cos(C) = 21/84
cos(C) = 0.25
Now, we can use the inverse cosine function (cos^-1) to find angle C:
C = cos^-1(0.25)
C ≈ 75.5°
Since angle B is opposite side b, we have:
B = 180° - C
B ≈ 180° - 75.5°
B ≈ 104.5°
Therefore, the measure of angle B in triangle ABC is approximately 105° to the nearest degree.
To find the measure of angle B in triangle ABC, we can use the Law of Cosines, which states that in a triangle, the square of one side is equal to the sum of the squares of the other two sides minus twice their product, multiplied by the cosine of the included angle.
In this case, we can use the Law of Cosines to find angle B. Let's call it θ.
c^2 = a^2 + b^2 - 2*a*b*cos(θ)
Plugging in the given values:
8^2 = 7^2 + 6^2 - 2*7*6*cos(θ)
Simplifying:
64 = 49 + 36 - 84*cos(θ)
Solving for cos(θ):
84*cos(θ) = 49 + 36 - 64
84*cos(θ) = 21
cos(θ) = 21/84
cos(θ) = 0.25
Now, to find the value of θ, we need to take the inverse cosine (also called "arccosine") of 0.25.
θ = arccos(0.25)
Using a calculator, we find:
θ ≈ 75.52 degrees
Therefore, the measure of angle B in triangle ABC is approximately 76 degrees.