Question

find the value of trig function indicated, use Pythagorean theorem to find the third side if you need it. Part 4​

Answer 1

`\fbox{\begin{minipage}{5em}13. 0.830\\14. 0.800\\15. 0.391\\16. 0.750\end{minipage}}`

Explanation:

A right triangle with 3 sides: adjacent side, opposite side and hypotenuse (as shown in attached picture)

According to the trigonometric properties:

`sin(theta) = (opposite)/(hypotenuse)`

`cos(theta) = (adjacent)/(hypotenuse)`

`tan(theta) = (opposite)/(adjacent)`

`(adjacent)^(2) + (opposite)^(2) = (hypotenuse)^(2)`

`(adjacent)^(2) = (hypotenuse)^(2) - (opposite)^(2)`

`(opposite)^(2) = (hypotenuse)^(2) - (adjacent)^(2)`

Use the above formulas with corresponding sides:

`13) cos(theta) = (9)/(3√(13) ) = 0.83`

`14) sin(theta) = \frac{\sqrt{5^(2)-3^(2) } }{5} = (4)/(5) = 0.8`

`15) sin(theta) = \frac{9}{\sqrt{(8√(7)) ^(2) + 9^(2) } } = 0.391`

`16) tan(theta) = (3)/(4) = 0.75`

Hope this helps!

:)