Answer: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:
sine(angle)=(length of leg opposite the angle)/(length of hypotenuse)
cosine(angle)=(length of leg adjacent the angle)/(length of hypotenuse)
tangent(angle)=(length of leg opposite the angle)/(length of leg adjacent the angle)
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:
tangent(34)=(8 ft)/(distance)
Solving:
distance× tangent(34)= 8 ft
distance=(8 ft)/(tangent(34))
distance= 11.86 ft
Finally, the distance from the ball to the goal is 11.86 ft.
The angle of elevation from a soccer ball on the - 1
