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Find the trigonometric ratio using the diagram. Write the fraction in itssimplest form.

Find the trigonometric ratio using the diagram. Write the fraction in itssimplest-example-1
User Warp
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1 Answer

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18 votes

Answer

KM = 30 units

Tan M = (8/15)

Step-by-step explanation

The Pythagoras Theorem is used for right angled triangle, that is, triangles that have one of their angles equal to 90 degrees.

The side of the triangle that is directly opposite the right angle or 90 degrees is called the hypotenuse. It is normally the longest side of the right angle triangle.

The Pythagoras theorem thus states that the sum of the squares of each of the respective other sides of a right angled triangle is equal to the square of the hypotenuse. In mathematical terms, if the two other sides are a and b respectively,

a² + b² = (hyp)²

For this question,

a = KM = ?

b = KL = 16

hyp = LM = 34

a² + b² = (hyp)²

KM² + 16² = 34²

KM² + 256 = 1,156

KM² = 1,156 - 256

KM² = 900

Take the square root of both sides

√(KM²) = √(900)

KM = 30 units

In a right-angle triangle, the side opposite the right angle is the Hypotenuse, the side opposite the given angle that is non-right angle is the Opposite and the remaining side is the Adjacent.

Using M as the given non-right angle,

Hypotenuse = LM = 34

Opposite = KL = 16

Adjacent = KM = 30

Using trignometric identities, we know that TOA means

Tan M = (Opp/Adj)

Tan M = (16/30)

Divide numerator and denominator by 2

Tan M = (16/30) = (8/15)

Hope this Helps!!!

User Sdds
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