Respuesta :
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.
Explanation:
To find x :
The value of x can be calculated using the trigonometric ratio of tan.
[tex]\begin{gathered} \tan \theta=\frac{\text{opposite}}{\text{adjacent}} \\ \tan 45\degree=\frac{x}{4} \\ 1=\frac{x}{4} \\ x=4 \\ AB=4 \end{gathered}[/tex]To find h :
The value of h can be calculated using the Pythagorean theorem.
[tex]\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}[/tex]Hence, the measure of length AB is 4 and the measure of length BC is 4√2.
