Question

Determine the numerical values of the trigonometric ratios of the acute angle of 45°-45°-90° triangle.

Answer 1

`\begin{gathered} \sin45=(√(2))/(2) \\ \cos45=(√(2))/(2) \\ \tan45=1 \end{gathered}`

Step-by-step explanation:

Given:

45°-45°-90° triangle.​

To find:

The numerical values of the trigonometric ratios.

Let's sketch the given triangle;

Since sides AC and CB are congruent, we can choose the length of their sides to be 1 and go ahead and solve for the length of side AB which is x using the Pythagorean theorem as seen below;

`\begin{gathered} x^2=1^2+1^2 \\ x^2=1+1 \\ x^2=2 \\ x=√(2) \end{gathered}`

We can now determine the values of each trigonometric ratio as seen below;

`\sin45=\frac{opposite\text{ side to angle 45}}{hypotenuse}=(1)/(√(2))=(1*√(2))/(√(2)*√(2))=(√(2))/(2)`
`\cos45=\frac{adjacent\text{ side to angle 45}}{hypotenuse}=(1)/(√(2))=(1*√(2))/(√(2)*√(2))=(√(2))/(2)`
`\tan45=\frac{opposite\text{ side to angle 45}}{adjacent\text{ side to angle 45}}=(1)/(1)=1`