Answer:
In the given scenario, you can consider the ladder, the wall, and the ground as forming a right-angled triangle. The length of the ladder is the hypotenuse, the height of the wall is one of the legs, and the distance from the base of the ladder to the base of the wall is the other leg.
The trigonometric ratio that involves the opposite side and the adjacent side in a right-angled triangle is the tangent (tan) of an angle. The formula for tangent is:
tan(θ)= Adjacent / Opposite
In this case, if we let θ be the angle formed by the ladder and the ground, then the length of the ladder (13 feet) is the hypotenuse, the height of the wall (12 feet) is the opposite side, and the distance from the base of the ladder to the base of the wall (5 feet) is the adjacent side.
Therefore, the trigonometric ratio tan(θ) is given by:
tan (θ) = Adjacent / Opposite = 12 / 5
So, in this scenario, the trigonometric ratio with the value 12 / 5 is the tangent of the angle formed by the ladder and the ground.
OR
The trigonometric ratio that has the value 12/5 in the context of the given information about the ladder leaning against the wall is the tangent. This can be determined from the relationship between the sides of a right-angled triangle and the tangent function. In this case, the tangent of the angle θ is equal to the ratio of the opposite side (the height of the wall, which is 12 feet) to the adjacent side (the distance from the base of the ladder to the base of the wall, which is 5 feet). Therefore, tan θ = 12/5
Step-by-step explanation:
