Question

The question is in the picture the unknown side length a is =sin B =cos B =tan B =sec B=csc B=cot B=

Answer 1

In a right triangle you use te Pythagorean theoren:

`c^2=a^{_{}2}+b^2`

As you have the value of sides b and c, solve the equation fot a:

`\begin{gathered} a^2=c^2-b^2 \\ a=\sqrt[]{c^2-b^2} \end{gathered}`

b= 4

c= 7

`a=\sqrt[]{7^2-4^2}=\sqrt[]{49-16}=\sqrt[]{33}`

Trigonometric functions for angle B.

Being a the adjacent and b the opposite, c is the hypotenuse. To rationalizing the denominator multiply the fraction by a fraction with the radical in numerator and denominator:

`\begin{gathered} \sin B=(b)/(c)=(4)/(7) \\ \end{gathered}`
`\cos B=(a)/(c)=\frac{\sqrt[]{33}}{7}`
`\tan B=(b)/(a)=\frac{4}{\sqrt[]{33}}\cdot\frac{\sqrt[]{33}}{\sqrt[]{33}}=\frac{4\cdot\sqrt[]{33}}{33}`
`\csc B=(c)/(b)=(7)/(4)`
`\sec B=(c)/(a)=\frac{7}{\sqrt[]{33}}\cdot\frac{\sqrt[]{33}}{\sqrt[]{33}}=\frac{7\cdot\sqrt[]{33}}{33}`
`\cot B=(a)/(b)=\frac{\sqrt[]{33}}{4}`