Respuesta :

Answer:

see explanation

Step-by-step explanation:

The missing angle is 45°, thus the right triangle is isosceles.

Then the 2 sides y and 7 are congruent.

Hence y = 7

Using Pythagoras' identity to calculate x

x² = 7² + 7² = 49 + 49 = 98

Take the square root of both sides

x = [tex]\sqrt{98}[/tex] = [tex]\sqrt{49(2)}[/tex] = 7[tex]\sqrt{2}[/tex] ≈ 10

Solution:

Step-1. Find the missing angle

We know that:

  • Sum of the angles of the triangle = 180°

This means that:

  • 45 + x + 90 = 180°

Now, let's simplify the equation to find the missing angle.

  • x + 135 = 180°
  • x + 135 - 135 = 180 - 135
  • x = 45°

Thus, the missing angle is 45°.

Step-2. Finding "y"

Classifying the triangle:

  • In the triangle, we see that the base angles are the same. This means that the triangle is isosceles.

~No further explanation about the triangle is required~

Finding the measure of y:

  • Since the triangle is isosceles, the length of y is 7 units because the legs of the isosceles triangle are equal.

Step-3: Finding "x"

To find "x", we need to use Pythagoras theorem.

Formula: c² = b² + a²

  • c = largest side (x)
  • b = leg side (7)
  • a = leg side (7)

Using Pythagoras theorem:

  • (x)² = (7)² + (7)²
  • (x)² = 49 + 49
  • (x)² = 98
  • x = √98 = √49 × 2 = 7√2 ≈ 9.89 ≈ 9.9 (Nearest tenth)

Conclusion:

  • y = 7
  • x = 9.9 (Nearest tenth)