Question

Use the properties of 30-60-90 and 45-45-90 triangles to solve for x in each of the problems below. Then decode the secret message by matching the answer with the corresponding letter/symbol from the exercises. Triangle T.

Answer 1

We need to find the value of x for the triangle:

Notice that this triangle has a right angle (90º), which is represented by the square marking.

Also, it has two congruent angles, which are represented by the same markings.

Since the internal angles of a triangle must add up to 180º, those acute angles measure 45º each:

`90\degree+45\degree+45\degree=180\degree`

Now, for this 45-45-90 triangle, we have:

`\frac{\text{ opposite leg}}{\text{ hypotenuse}}=\frac{\text{ adjacent leg}}{\text{ hypotenuse}}=(1)/(√(2))`

Thus, we have:

`\begin{gathered} (x)/(√(10))=(1)/(√(2)) \\ \\ (√(10))/(√(10))x=(√(10))/(√(2)) \\ \\ x=(√(2)\cdot√(5))/(√(2)) \\ \\ x=√(5) \end{gathered}`

Answer:

`x=√(5)`