Question

Find x. Leave answers in simplified radical form. (Step by step)

Answer 1

Step-1: Find the missing angle.

• 90 + 45 + y = 180
• => 135 + y = 180
• => y = 180 - 135
• => y = 45°

Step-2: Review the following.

• This triangle is an isosceles right triangle because two angles are equivalent.
• Two sides of the triangle must equal 4 cm.

Step-3: Use Pythagoras theorem.

• x² = 4² + 4²
• => x² = 16 + 16
• => x = √32 ≈ 5.65 cm (Using calculator)

Answer 2

`\sf x = 4√(2)`

Given:

• adjacent: 4 cm
• hypotenuse: x cm
• angle: 45°

using cosine rule:

`\sf cos(x) = (adjacent)/(hypotenuse)`

`\sf cos(45) = (4)/(x)`

`\sf x = (4)/(cos(45))`

`\sf x = 4√(2)`