Answer
Sin E = (21/29)
Cos E = (20/29)
Tan E = (21/20)
Step-by-step explanation
To answer this, we need to first find the third side of this triangle.
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 = EF = 20
b = DF = ?
hyp = DE = 29
a² + b² = (hyp)²
20² + b² = 29²
400 + b² = 841
b² = 841 - 400
b² = 441
Take the square root of both sides,
√(b²) = √(441)
b = 21
So, now that we have all the sides, we can write the trignometric ratios
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 angle is the Opposite and the remaining side is the Adjacent.
For this question,
Hypotenuse = DE = 29
Opposite = DF = 21
Adjacent = EF = 20
Angle = E
Trignometric ratios of SOH, CAH and TOA allow us to interprete these as
Sin E = (Opp/Hyp)
Sin E = (21/29)
Cos E = (Adj/Hyp)
Cos E = (20/29)
Tan E = (Opp/Adj)
Tan E = (21/20)
Hope this Helps!!!