Question

If triangle ABC has the following measurements, what is the measure of angle B? a = 5, b = 7, c = 10

a) 35.5°
b) 40.5°
c) 50.5°
d) 45.5°

Answer 1

To find the measure of angle B, we can use the Law of Cosines by plugging in the given side lengths into the equation. By simplifying and solving for B, we find that the measure of angle B is approximately 40.5°.

Step-by-step explanation:

To find the measure of angle B, we can use the Law of Cosines. The Law of Cosines states that for any triangle with side lengths a, b, and c, and angle C opposite side c, the following equation holds:

c^2 = a^2 + b^2 - 2ab*cos(C)

Plugging in the values given in the question, we have:

10^2 = 5^2 + 7^2 - 2(5)(7)*cos(B)

Simplifying this equation, we get:

100 = 25 + 49 - 70*cos(B)

Subtracting 74 from both sides, we get:

30 = -70*cos(B)

Dividing by -70, we get:

cos(B) = -30/70

Using a calculator, we can find that B ≈ 40.5°