In the diagram, point D divides line segment AB in the ratio of 5:3. If line segment AC is vertical and line segment CD is horiz
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Answer:
See below for explanation
Step-by-step explanation:
A related question can be found at chegg. Find attached the diagram.
The triangle is a right angled triangle. The 3 sides are named opposite, adjacent and hypotenuse.
The opposite is the vertical side facing angle theta (θ)
The adjacent is horizontal side
The angle between opposite and adjacent = 90°
The hypotenuse is the longest side
The relationship between the 3 sides:
Hypotenuse² = opposite ² + adjacent²
The relationship between theta (θ)
and the lengths of the sides of the triangle:
Applying SOHCAHTOA in trigonometry
Sine ratio:
Sinθ = opposite/hypotenuse
Cosine ratio:
Cosθ = adjacent/hypotenuse
Tangent ratio:
Tanθ = opposite/adjacent
Applying the Pythagorean theorem to find the third side of the triangle
Hypotenuse² = opposite ² + adjacent²
Hypotenuse = 7, opposite = 4
adjacent² = Hypotenuse² - opposite ²
adjacent² = 7²-4² = 49-16
adjacent² = 33
Adjacent = √33
Write out the six trigonometric functions in exact form related to theta.
cosθ = adjacent/hypotenuse = (√33)/7
sinθ = opposite/hypotenuse = 4/7
tanθ = sinθ/cosθ = opposite/adjacent
sinθ/cosθ = 4/7 ÷ (√33)/7
= 4/7 × 7/(√33) = 4/(√33)
opposite/adjacent = 4/(√33)
tanθ = 4/(√33)
secθ = 1/cosθ = 1/(√33)/7
= 7/√33
cosecθ = 1/sinθ = 1/(4/7)
= 1×7/4 = 7/4
cotθ = 1/tanθ = 1/[4/(√33)]
cotθ =(√33)/4
