Given:
The given triangle is right angled triangle.
The angle is 45 degrees.
The adjacent side is 15.
Required:
We need to find the hypotenuse of the given triangle.
Explanation:
Consider the cosine formula.
[tex]cos\theta=\frac{adjacent\text{ side}}{hypotenuse}[/tex][tex]Substitute\text{ }\theta=45\degree\text{ and adjacent side=15 in the formula.}[/tex][tex]cos45\degree=\frac{15}{hypotenuse}[/tex][tex]hypotenuse=\frac{15}{cos45\degree}[/tex][tex]Use\text{ }cos45\degree=\frac{\sqrt{2}}{2}\text{ in the equation.}[/tex][tex]hypotenuse=\frac{15}{\frac{\sqrt{2}}{2}}[/tex][tex]hypotenuse=15\times\frac{2}{\sqrt{2}}[/tex][tex]hypotenuse=15\times\frac{\sqrt{2}\times\sqrt{2}}{\sqrt{2}}[/tex][tex]hypotenuse=15\times\sqrt{2}[/tex][tex]hypotenuse=15\sqrt{2}[/tex]
Final answer:
[tex]hypotenuse=15\sqrt{2}[/tex]
