Considering the trigonometric relationships, the distance from the ball to the goal is 11.86 ft.
The right triangle is a three-sided polygon that has one of its right angles, that is, it measures 90 °, while the remaining two angles are less than a right angle, but add up to 90 °.
The elements of a right triangle are: the two sides contiguous to the right angle called legs, and the longest side, opposite the right angle, which is the hypotenuse.
Trigonometric relationships are special measures of a right triangle. Remember that the two sides of a right triangle that form the right angle are called the legs, and the third side (opposite the right angle) is called the hypotenuse.
There are three basic trigonometric relationships: sine, cosine, and tangent, which are defined as:
- [tex]sine(angle)=\frac{length of leg opposite the angle}{length of hypotenuse}[/tex]
- [tex]cosine(angle)=\frac{length of leg adjacent the angle}{length of hypotenuse}[/tex]
- [tex]tangent(angle)=\frac{length of leg opposite the angle}{length of leg adjacent the angle}[/tex]
In this case, the trigonometric relation used is the tangent, where:
- angle= 34 degrees
- length of leg opposite the angle= 8 ft
- length of leg adjacent the angle= distante
Replacing in the definition:
[tex]tangent(34)=\frac{8 ft}{distance}[/tex]
Solving:
distance× tangent(34)= 8 ft
[tex]distance=\frac{8 ft}{tangent(34)}[/tex]
distance= 11.86 ft
Finally, the distance from the ball to the goal is 11.86 ft.
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