Question

Use special right triangles to solve for the value of x.

Answer 1

Answer

7

Explanation.

The triangle shown is a right triangle. One of the acute angles is given as 45°. Angles in a triangle add up to 180°

So we can get the third angle of the triangle as follows:

180 - (90+45) = 45.

From this we can conclude that, apart from the triangle being an right triangle, it is also isosceles triangle. This means that the two shorter sides of the triangle are equal.

So, the value of x is 7.

Answer 2

Answer: x = 7

Explanation:

1) This special right triangle is the isosceles right triangle: 45°-45°-90°.

It is an isosceles right triangle, then x = 7.

2) For these the isosceles right triangle you have: hypotenuse = leg length × √2.

You can prove that using Pythagoras: hypotenuse² = side² + side² = 2×side² ⇒ hypotenuse.

3) Therefore: x = 7 and y = 7√2