Question

The shape of a garden is shown as the following figure...

Answer 1

For a triangle with all three sides given, we can determine the size/measure of one of the angles by using the law of cosines.

The law of cosines is given as follows;

`a^2=b^2+c^2-2bc\cos A`

Where the variables are;

`A=\theta,a=160,b=90,c=180`

We can plug in the values into the cosine formula and we'll have;

`\begin{gathered} 160^2=90^2+180^2-2(90)(180)\cos A \\ 25600=8100+32400-32400\cos A \\ 25600=40500-32400\cos A \\ \text{Subtract 40500 from both sides;} \\ -14900=-32400\cos A \\ \text{Divide both sides by -32400} \\ (-14900)/(-32400)=\cos A \\ \cos A=0.4598765 \\ \end{gathered}`

To determine the angle measure of the result above, we now look up the value of arc-cos 0.4598765 on a calculator, and we'll have;

`\begin{gathered} \cos A=0.4598765 \\ A=\cos ^(-1)0.4598765 \\ A=62.62086 \\ \text{Rounded to one decimal point} \\ A=62.6 \end{gathered}`

ANSWER:

The indicated angle measures 62.6 degrees