Given:
Record the lengths of two of the sides of the triangle and the measure of the included angle.
To find:
The measurements of the triangle ∆ABC.
Explanation:
Here, the base of the triangle is 8 cm.
Let us draw the perpendicular line BD intersecting AC at D.
The height of the triangle is 4 cm.
The length of the other two sides needs to be found.
Using the Pythagoras theorem,
[tex]\begin{gathered} Hyp^2=Opp^2+adj^2 \\ AB^2=AD^2+BD^2 \\ AB^2=4^2+4^2 \\ AB^2=32 \\ AB=\sqrt{32} \\ AB=4\sqrt{2}cm \\ \therefore BC=4\sqrt{2}cm \end{gathered}[/tex]
Let's find the angle A using the triangle ABD,
[tex]\begin{gathered} tanA=\frac{BD}{AD} \\ tanA=\frac{4}{4} \\ tanA=1 \\ A=45^{\circ} \\ \therefore B=45^{\circ} \end{gathered}[/tex]
Final answer:
Two sides are,
[tex]\begin{gathered} AB=4\sqrt{2}cm \\ AC=8cm \end{gathered}[/tex]
The included angle is,
[tex]A=45^{\circ}[/tex]
