Question

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

Answer 1

ANSWER

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

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:

$\tan A=\frac{opposite}{adjacent}$

Therefore, we have:

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

That is the answer.