Question

what is a ? Do not include units (degrees) in your answer.

Answer 1

Explanation

Step 1

we have a right triangle,find the hypotenuse

use Pythagoras Teorem to find the hypotenuse ( green line)

$\begin{gathered} T\mathrm{}P\text{. } \\ \text{adjacent side}^2+oppositeside^2=hypotenuse^2 \end{gathered}$

replacing

$\begin{gathered} \text{red line}^2+blueline^2=greenline^2 \\ 3^2+12^2=hypotenuse^2 \\ 9+144=hypotenuse^2 \\ hypotenuse^2=153 \\ hypotenuse=\sqrt[]{153} \\ \\ \end{gathered}$

Step

use cosine function to find the angles

a)

$\cos \beta=\frac{adjacent\text{ side}}{\text{hypotenuse}}$

replace,

$\begin{gathered} \text{angle}=\alpha \\ \text{adjacen side =3} \\ \text{hypotenuse = }\sqrt[]{153} \\ \cos \alpha=\frac{3}{\sqrt[]{153}} \\ \text{then} \\ \alpha=\cos ^{-1}(\frac{3}{\sqrt[]{153}}) \end{gathered}$

b)

$\begin{gathered} \text{angle}=\emptyset \\ \text{adjacent side = 12} \\ \text{hypotenuse}=\sqrt[]{153} \\ \text{then} \\ \cos \emptyset=\frac{12}{\sqrt[]{153}} \\ \emptyset=\cos ^{-1}(\frac{12}{\sqrt[]{153}}) \end{gathered}$