Question

Find the measure of angle Aa=26.61 km, b= 21.46 km, c= 19.62 km

Answer 1

The value of angle A is 80.61°

Explanation:

Given:

a=26.61 km,

b= 21.46 km

c= 19.62 km

We can calculate the value of angle A by means of the law of cosines, which is as follows:

`a^2=b^2+c^2-2\cdot b\cdot c\cdot\cos(A)`

We solve for A and then substitute to calculate it, like this:

`\begin{gathered} 2\cdot b\cdot c\cdot\cos(A)=b^2+c^2-a^2 \\ \\ \cos(A)=(b^2+c^2-a^2)/(2\cdot b\cdot c) \\ \\ A=\cos^(-1)\left(\:(b^2+c^2-a^2)/(2\cdot\:b\cdot\:c)\:\right) \\ \\ \text{ We repalcing} \\ \\ A=\cos^(-1)\left(\:(21.46^2+19.62^2-26.61^2)/(2\cdot\:21.46\cdot\:19.62)\:\right) \\ \\ A=\cos^(-1)(0.1631) \\ \\ A=80.61\degree \end{gathered}`

The value of angle A is 80.61°