Question

error analysis describe the error in the statement of the tangent ratio. correct the error if possible. otherwise, write not possible.
image of a right triangle def with right angle at e, de=12, ef=35, df=37, and the incorrect statement tan d = 35/37

Explanation:

Step1: Recall the tangent ratio definition

In a right triangle, the tangent of an acute angle is the ratio of the length of the opposite side to the length of the adjacent side. For angle \( D \) in right triangle \( DEF \) (right - angled at \( E \)):

• Opposite side to \( \angle D \): \( EF = 35 \)
• Adjacent side to \( \angle D \): \( DE=12 \)
• Hypotenuse: \( DF = 37 \) (we should not use the hypotenuse in the tangent ratio)

The formula for \( \tan D \) is \( \tan D=\frac{\text{opposite}}{\text{adjacent}}=\frac{EF}{DE} \)

Step2: Identify the error

The given expression for \( \tan D \) is \( \frac{35}{37} \), which uses the hypotenuse (\( 37 \)) instead of the adjacent side (\( 12 \)) in the denominator.

Step3: Correct the tangent ratio

Using the correct formula \( \tan D=\frac{\text{opposite}}{\text{adjacent}} \), with opposite \( = 35 \) and adjacent \( = 12 \), we get \( \tan D=\frac{35}{12} \)

Answer:

The error is that the tangent ratio for \( \angle D \) was calculated using the hypotenuse (37) instead of the adjacent side (12) to \( \angle D \). The correct tangent ratio is \( \tan D=\frac{35}{12} \)