Question

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

Answer 1

Answer:

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

Step-by-step explanation:

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

According to the trigonometric properties:

$sin(theta) = \frac{opposite}{hypotenuse}$

$cos(theta) = \frac{adjacent}{hypotenuse}$

$tan(theta) = \frac{opposite}{adjacent}$

$(adjacent)^{2} + (opposite)^{2} = (hypotenuse)^{2}$

$(adjacent)^{2} = (hypotenuse)^{2} - (opposite)^{2}$

$(opposite)^{2} = (hypotenuse)^{2} - (adjacent)^{2}$

Use the above formulas with corresponding sides:

$13) cos(theta) = \frac{9}{3\sqrt{13} } = 0.83$

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

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

$16) tan(theta) = \frac{3}{4} = 0.75$

Hope this helps!

:)