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Verizon [17]
3 years ago
8

Use the Law of Cosines to find the values of x and y. (PLEASE HELPPP!!!!)

Mathematics
1 answer:
vredina [299]3 years ago
7 0

Answer:

x = 49.8^\circ\\y = 54.6^\circ

Step-by-step explanation:

Kindly refer to the image attached in the answer region for labeling of triangle.

<em>AB </em><em>= 16 </em>

<em>BC </em><em>= 19</em>

<em>AC </em><em>= 15 </em>

\angle ABC = x^\circ\\\angle ACB = y^\circ

We have to find the <em>angles </em><em>x</em> and <em>y</em> i.e. \angle B \text{ and }\angle C.

Formula for <em>cosine rule</em>:

cos B = \dfrac{a^{2}+c^{2}-b^{2}}{2ac}

Where  

<em>a</em> is the side opposite to \angle A,

<em>b</em> is the side opposite to \angle B  and

<em>c</em> is the side opposite to \angle C.

\Rightarrow cos x = \dfrac{19^{2}+16^{2}-15^{2}}{2 \times 19 \times 16}\\\Rightarrow cos x = \dfrac{392}{608} \\\Rightarrow x = 49.8^\circ

Similarly, for finding the value of <em>y:</em>

cos C = \dfrac{a^{2}+b^{2}-c^{2}}{2ab}\\\Rightarrow cos y = \dfrac{19^{2}+15^{2}-16^{2}}{2  \times 19 \times 15}\\\Rightarrow cos y = \dfrac{330}{570}\\\Rightarrow y = 54.6^\circ

Hence, the values are:

x = 49.8^\circ\\y = 54.6^\circ

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