Question

Find the qualities indicated without using the Pythagorean theorem.(Round to the nearest degree is needed)

Answer 1

`\begin{gathered} (a)A=45\degree \\ (b)c=14.1^(\prime) \end{gathered}`

Step-by-step explanation

First, let us find the value of c using the Pythagoras theorem:

`a^2+b^2=c^2`

where a and b are the other two legs of the triangle, and c is the hypotenuse

Therefore, we have that:

`\begin{gathered} 10^2+10^2=c^2 \\ \Rightarrow100+100=c^2 \\ 200=c^2 \\ \Rightarrow c=\sqrt[]{200} \\ c=14.1^(\prime) \end{gathered}`

Next, we find the measure of A by using the trigonometric ratios, SOHCAHTOA, of right angles:

`\tan A=(opposite)/(adjacent)`

Therefore, we have:

`\begin{gathered} \tan A=(10)/(10) \\ A=\tan ^(-1)(1) \\ A=45\degree \end{gathered}`

That is the answer.