Question

An electrician leans an extension ladder against the outside wall of a house so that it reaches an electric box 34 feet up. The ladder makes an angle of 63

∘
∘
with the ground. Find the length of the ladder. Round your answer to the nearest tenth of a foot if necessary.

Answer 1

Explanation:

The answer is 38.2 Feet long

.

Draw a diagram. Label givens. Label unknown x.

34

x

63°

I

34

x

63°

(hypotenuse)

What function uses the

OPPOSITE

and the

HYPOTENUSE

?

What function uses the OPPOSITE and the HYPOTENUSE?

S

‾

O

H

-CAH-TOA

S

​

OH-CAH-TOA

sin

63

=

opposite

hypotenuse

=

34

�

sin 63=

hypotenuse

opposite

​

=

x

34

​

sin

63

=

sin 63=

 

 

34

�

x

34

​

sin

63

1

=

1

sin 63

​

=

 

 

34

�

x

34

​

�

sin

63

=

x sin 63=

 

 

34

34

Cross multiply.

�

sin

63

sin

63

=

sin 63

x sin 63

​

=

 

 

34

sin

63

sin 63

34

​

Divide both sides by sin 63

�

=

34

sin

63

=

38.159092...

≈

38.2

x=

sin 63

34

​

=38.159092...≈38.2

Answer 2

Sure, I can help you with that.

We can use the Pythagorean Theorem to solve for the length of the ladder. The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, the hypotenuse is the length of the ladder, and the other two sides are the distance to the electric box and the height of the ladder.

So, we have:

```

(length of ladder)^2 = (distance to electric box)^2 + (height of ladder)^2

```

```

(length of ladder)^2 = 34^2 + 34^2

```

```

(length of ladder)^2 = 2 * 34^2

```

```

length of ladder = sqrt(2 * 34^2)

```

```

length of ladder = 34 * sqrt(2)

```

```

length of ladder = 57.2 feet (rounded to the nearest tenth)

```

Therefore, the length of the ladder is 57.2 feet.