Given:
A right triangle has a hypotenuse of length 5.00 m, and one of its angles is 40.0°.
Required:
a) the side opposite the 40.0° angle.
(b) the side adjacent to the 40.0° angle.
Explanation:
First draw a picture
Now, the trigonometric ratios
[tex]cos\theta=\frac{base}{hypotenuse},sin\theta=\frac{Perpendicular}{Hypotenuse}[/tex]So,
(a) The side opposite the 40.0° angle
[tex]\begin{gathered} sin(40^{\circ})=\frac{P}{5} \\ P=5\times sin(40^{\circ}) \\ P=3.2 \end{gathered}[/tex]and
(b) The side adjacent to the 40.0° angle
[tex]\begin{gathered} cos(40^{\circ})=\frac{b}{5} \\ b=5\times cos(40^{\circ}) \\ b=3.8 \end{gathered}[/tex]Answer:
The side opposite to 40 degree angle equal 3.2 m and side adjacent equal 3.8 m.
