Question

Need help with homework

Answer 1

Given:

The length of the side AC = 4.

The measure of angle m∠C = 45°.

The measure of angle m∠B = 45°.

The objective is to find the measure of length AB and BC.

Step-by-step explanation:

To find x :

The value of x can be calculated using the trigonometric ratio of tan.

`\begin{gathered} \tan \theta=\frac{\text{opposite}}{\text{adjacent}} \\ \tan 45\degree=(x)/(4) \\ 1=(x)/(4) \\ x=4 \\ AB=4 \end{gathered}`

To find h :

The value of h can be calculated using the Pythagorean theorem.

`\begin{gathered} h=\sqrt[]{AC^2+AB^2} \\ =\sqrt[]{4^2+4^2} \\ =\sqrt[]{16+16} \\ =\sqrt[]{32} \\ =4\sqrt[]{2} \\ BC=4\sqrt[]{2} \end{gathered}`

Hence, the measure of length AB is 4 and the measure of length BC is 4√2.