Example 2: Triangle DEF .Given: $$ \circ $$ Hypotenuse $$ \mathrm{DE}=13 \mathrm{~cm} $$. $$ \circ $$ One leg $$ \mathrm{DF}=5 \mathrm{~cm} $$. $$ \circ \angle \mathrm{F}=90 $$

Question

UpStudy AI · Accepted Answer

To solve the problem involving triangle DEF, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). The formula is given by:

$$
c^2 = a^2 + b^2
$$

In this case:
- The hypotenuse $$ DE = 13 \, \text{cm} $$ (which we will denote as $$ c $$).
- One leg $$ DF = 5 \, \text{cm} $$ (which we will denote as $$ a $$).
- We need to find the length of the other leg $$ EF $$ (which we will denote as $$ b $$).

### Step 1: Set up the equation

Using the Pythagorean theorem, we can set up the equation as follows:

$$
DE^2 = DF^2 + EF^2
$$

Substituting the known values:

$$
13^2 = 5^2 + EF^2
$$

### Step 2: Calculate the squares

Calculating the squares:

$$
169 = 25 + EF^2
$$

### Step 3: Solve for $$ EF^2 $$

Now, we can isolate $$ EF^2 $$:

$$
EF^2 = 169 - 25
$$

Calculating the right side:

$$
EF^2 = 144
$$

### Step 4: Find $$ EF $$

Now, we take the square root of both sides to find $$ EF $$:

$$
EF = \sqrt{144}
$$

Calculating the square root:

$$
EF = 12 \, \text{cm}
$$

### Conclusion

The length of the other leg $$ EF $$ is $$ 12 \, \text{cm} $$. Thus, the dimensions of triangle DEF are:
- Hypotenuse $$ DE = 13 \, \text{cm} $$
- Leg $$ DF = 5 \, \text{cm} $$
- Leg $$ EF = 12 \, \text{cm} $$
The length of the other leg $$ EF $$ is $$ 12 \, \text{cm} $$.

Example 2: Triangle DEF
.Given:
Hypotenuse .
One leg .

Solución de inteligencia artificial de Upstudy

Responder

Solución

Step 1: Set up the equation

Step 2: Calculate the squares

Step 3: Solve for

Step 4: Find

Conclusion

Mind Expander

preguntas relacionadas

Latest Geometry Questions

Example 2: Triangle DEF .Given: Hypotenuse . One leg .