Question

Triangle has three sides 12 17 and 24 find the measure of angle B

Answer 1

The given side lengths of 12, 17, and 24 give a unique triangle from which the measure of angle ∠B, taken as the angle opposite the side of length 17, and found using cosine rule, is approximately 41.56°

What is the law of cosines?

The law of cosines states that the the square of the length of a side of a triangle is given by the sum of the square of the other two sides, less the product of two and the other two sides, and the cosine of the angle between them

Mathematically, a²= b² + c² - 2·b·c·cos(A)

The given lengths of the sides are; 12, 17 and 24

The measure of the angles are given by the law of cosines as follows;

a² = b² + c² - 2·b·c·cos(A)

Which gives;

2·b·c·cos(A) = b² + c² - a²

Which gives;

$cos(A) = \dfrac{b^2 + c^2 - a^2}{2\cdot b \cdot c}$

Let a = 12, b = 17, and c = 24, we have;

$cos(A) = \dfrac{17^2 + 24^2 - 12^2}{2\times 17 \times 24} =\dfrac{721}{816}$

$A = arcos\left(\dfrac{721}{816}\right)\approx 27.9^{\circ}$

Similarly, we have;

$cos(B) = \dfrac{a^2 + c^2 - b^2}{2\cdot a \cdot c}$

$cos(B) = \dfrac{12^2 + 24^2 - 17^2}{2\times 12 \times 24} = \dfrac{431}{576}$

$B= arcos\left( \dfrac{431}{576}\right)\approx 41.56^{\circ}$

• The measure of angle ∠B is approximately 41.56°

Learn more about the law of cosines here:

brainly.com/question/2491835

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