Question

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Answer 1

x = 8√2

Explanation:

As the opposing side of the angle and the hypotenuse are given, take the sine ratio of the angle.

• sin 45° = x/16
• 1/√2 = x/16
• x = 16 / √2
• x = 16√2 / 2
• x = 8√2

Answer 2

`\sf x=8{√(2)`

Explanation:

Trigonometric ratios

`\sf \sin(\theta)=(O)/(H)\quad\cos(\theta)=(A)/(H)\quad\tan(\theta)=(O)/(A)`

where:

• 
  `\theta` is the angle
• O is the side opposite the angle
• A is the side adjacent the angle
• H is the hypotenuse (the side opposite the right angle)

Therefore, to find x we need to use the sine trig ratio.

Given:

• 
  `\theta` = 45°
• O = x
• H = 16

Substitute these values into the formula and solve for x:

`\implies \sf \sin(\theta)=(O)/(H)`

`\implies \sf \sin(45^(\circ))=(x)/(16)`

`\implies \sf x=16 \sin(45^(\circ))`

`\implies \sf x=16 \cdot (√(2))/(2)`

`\implies \sf x=8{√(2)`