Question

X = ? y = ? 16 45 degrees

Answer 1

Let's put more details in the figure to better understand the problem:

Let's first recall the three main trigonometric functions:

$\text{ Sine }\theta\text{ = }\frac{\text{ Opposite Side}}{\text{ Hypotenuse}}$$\text{ Cosine }\theta\text{ = }\frac{\text{ Adjacent Side}}{\text{ Hypotenuse}}$$\text{ Tangent }\theta\text{ = }\frac{\text{ Opposite Side}}{\text{ Adjacent Side}}$

For x, we will be using the Cosine Function:

$\text{ Cosine }\theta\text{ = }\frac{\text{ Adjacent Side}}{\text{ Hypotenuse}}$$Cosine(45^{\circ})\text{ = }\frac{\text{ x}}{\text{ 1}6}$$(16)Cosine(45^{\circ})\text{ = x}$$(16)(\frac{1}{\sqrt[]{2}})\text{ = x}$$\text{ }\frac{16}{\sqrt[]{2}}\text{ x }\frac{\sqrt[]{2}}{\sqrt[]{2}}\text{ = }\frac{16\sqrt[]{2}}{2}$$\text{ 8}\sqrt[]{2}\text{ = x}$

Therefore, x = 8√2.

For y, we will be using the Sine Function.

$\text{ Sine }\theta\text{ = }\frac{\text{ Opposite Side}}{\text{ Hypotenuse}}$$\text{ Sine }(45^{\circ})\text{ = }\frac{\text{ y}}{\text{ 1}6}$$\text{ (16)Sine }(45^{\circ})\text{ = y}$$\text{ (16)(}\frac{1}{\sqrt[]{2}})\text{ = y}$$\text{ }\frac{16}{\sqrt[]{2}}\text{ x }\frac{\sqrt[]{2}}{\sqrt[]{2}}\text{ = }\frac{16\sqrt[]{2}}{2}$$\text{ 8}\sqrt[]{2}\text{ = y}$

Therefore, y = 8√2.