Question

I need help with this:Create a random triangle, ∆ABC. Record the lengths of two of the sides of the triangle and the measure of the included angle.

Answer 1

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.

Step-by-step 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,

`\begin{gathered} Hyp^2=Opp^2+adj^2 \\ AB^2=AD^2+BD^2 \\ AB^2=4^2+4^2 \\ AB^2=32 \\ AB=√(32) \\ AB=4√(2)cm \\ \therefore BC=4√(2)cm \end{gathered}`

Let's find the angle A using the triangle ABD,

`\begin{gathered} tanA=(BD)/(AD) \\ tanA=(4)/(4) \\ tanA=1 \\ A=45^(\circ) \\ \therefore B=45^(\circ) \end{gathered}`

Final answer:

Two sides are,

`\begin{gathered} AB=4√(2)cm \\ AC=8cm \end{gathered}`

The included angle is,

`A=45^(\circ)`