In `DeltaDEF` measure of angle E is `90^(@)`.If `cotD=(5)/(12)`,and DE =1 cm, what is the ,length (in cm.)of side EF ?

Options

A. 2.4
B. 2.6
C. 1.5
D. 2

Answer

To solve the problem, we will follow these steps:

### Step 1: Understand the triangle and given values
In triangle DEF, angle E is 90 degrees. We are given that \( \cot D = \frac{5}{12} \) and \( DE = 1 \) cm.

### Step 2: Use the definition of cotangent
The cotangent of an angle in a right triangle is defined as the ratio of the adjacent side to the opposite side. For angle D:
\[ \cot D = \frac{\text{Adjacent}}{\text{Opposite}} = \frac{DE}{EF} \]
Here, \( DE \) is the adjacent side to angle D, and \( EF \) is the opposite side.

### Step 3: Substitute the known values
We know:
\[ \cot D = \frac{5}{12} \quad \text{and} \quad DE = 1 \text{ cm} \]
Substituting these values into the cotangent definition gives us:
\[ \frac{DE}{EF} = \frac{5}{12} \]
This can be rewritten as:
\[ \frac{1}{EF} = \frac{5}{12} \]

### Step 4: Cross-multiply to solve for EF
Cross-multiplying gives us:
\[ 12 = 5 \cdot EF \]
Now, we can isolate \( EF \):
\[ EF = \frac{12}{5} \]

### Step 5: Calculate the value of EF
Calculating \( \frac{12}{5} \):
\[ EF = 2.4 \text{ cm} \]

### Final Answer
The length of side EF is \( 2.4 \) cm.

---