For the given triangle, x = 8 units and y = 11.3154 units.
Step-by-step explanation:
Step 1:
In the given triangle, the angle is 45° (the bottom right angle). It is given that the hypotenuse is y and the adjacent side is x. The opposite side of the triangle measures 8 units.
It is given that the hypotenuse measures y units and the adjacent side measures x units.
To determine the length of the hypotenuse of the triangle, we use the sin of the given angle.
To determine the length of the adjacent side of the triangle, we use the tan of the given angle.
Step 2:
In the given triangle,
The length of the opposite side = 8 units,
The length of the adjacent side = x units,
The length of the hypotenuse = y cm,
The angle of the triangle = 45°.
[tex]\begin{array}{l}\sin \theta=\frac{\text {oppositeside}}{\text {hypotenuse}}, \sin 45=\frac{8}{y}, \sin 45=0.707 \\\end{array}[/tex]
[tex]y = \frac{8}{0.707} = 11.3154.[/tex]
[tex]\begin{array}{l}\tan \theta=\frac{\text {opposite side}}{\text {adjacent side}}, \tan 45=\frac{8}{x}, \tan 45=1 \\\end{array}[/tex]
[tex]x = \frac{8}{1} = 8.[/tex]
So x = 8 units and y = 11.3154 units.
