9514 1404 393
Answer:
cot(θ) = 24/7
Step-by-step explanation:
A suitable calculator can answer this nicely.
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Perhaps you're expected to remember relevant trig identities.
tan(θ)^2 = sec(θ)^2 -1
cot(θ) = 1/tan(θ)
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cot(θ) = 1/√(sec(θ)^2 -1)
cot(θ) = 1/√((25/24)^2 -1) = 24/√(25^2 -24^2) = 24/√49
cot(θ) = 24/7
Here you haven't provided any function, so I'll assume this one:
This is a quadratic function whose graph represents a parabola. Any parabola has its vertex at the point:
Therefore:
Therefore, the vertex is:
The triangles formed by the path of the ball and the wall in the given diagram are similar triangles.
<h3>Correct Response;</h3>The point on the wall she should aim is; <u>A. 7.8 feet away from point B</u>
<h3 /><h3>Method by which the above value is obtained;</h3>The possible diagram in the question is attached
Let <em>x</em> represent the distance from point <em>B</em> where the ball lands.
ΔCDE is similar to ΔABE, by Angle-Angle similarity postulate.
By trigonometric ratio, the tangent of the angles ∠CDE and ∠BAE are;
tan(∠CDE) = tan(∠BAE)
Therefore;
Which gives;
16 × (20 - x) = 25·x
320 = 41·x
x = 320 ÷ 41 ≈ 7.8
The point on the wall she should aim if she's standing at point <em>A</em> is therefore;
Learn more about trigonometric ratios here:
