Question

A wooden board is leaning against a wall. The base of the board is 10 feet from the base of the wall. The base of the board forms a 35° angle with the ground.

What is the length of the wooden board?

Round your answer to nearest tenth.​

Answer 1

$\huge{\underline{\underbrace{\mathcal\color{green}{Question}}}}$

A wooden board is leaning against a wall. The base of the board is 10 feet from the base of the wall. The base of the board forms a 35° angle with the ground.

• What is the length of the wooden board?
• answer will be rounded nearest ten

$\huge{\underline{\underbrace{\mathcal\color{gold}{☆Answer}}}}$

The length of the wooden board is about 12.2 feet.

explanation:

☆Please refer to the diagram attached below.

$\rightsquigarrow$ The base of the board forms a 35° degree angle with the ground.

And we want to find the length of the wooden board.

$\rightsquigarrow$ Since we are given an angle and its adjacent length and we want to find the hypotenuse, we can use the cosine ratio:

$\cos(\theta^\circ)=\dfrac{\text{adjacent}}{\text{hypotenuse}}$

$\rightsquigarrow$ The adjacent side is the distance from the wall to the board, which is 10 feet.

And the angle made is 35°.

The hypotenuse is the length of the wooden board.

$\rightsquigarrow$ Therefore:

$\displaystyle \cos(35)=\dfrac{10}{\ell}$

Solve for the length.

$\rightsquigarrow$ Cross-multiply:

$\displaystyle 10=\ell \cos(35)$

$\rightsquigarrow$ Therefore:

$\displaystyle \ell=\dfrac{10}{\cos(35)}\approx12.2$

The length of the wooden board is about 12.2 feet.

Answer 2

Answer:

The length of the wooden board is about 12.2 feet.

explanation:

☆Please refer to the diagram attached below.

\rightsquigarrow⇝ The base of the board forms a 35° degree angle with the ground.

And we want to find the length of the wooden board.

\rightsquigarrow⇝ Since we are given an angle and its adjacent length and we want to find the hypotenuse, we can use the cosine ratio:

\cos(\theta^\circ)=\dfrac{\text{adjacent}}{\text{hypotenuse}}cos(θ

∘

)=

hypotenuse

adjacent

\rightsquigarrow⇝ The adjacent side is the distance from the wall to the board, which is 10 feet.

And the angle made is 35°.

The hypotenuse is the length of the wooden board.

\rightsquigarrow⇝ Therefore:

\displaystyle \cos(35)=\dfrac{10}{\ell}cos(35)=

ℓ

10

Solve for the length.

\rightsquigarrow⇝ Cross-multiply:

\displaystyle 10=\ell \cos(35)10=ℓcos(35)

\rightsquigarrow⇝ Therefore:

\displaystyle \ell=\dfrac{10}{\cos(35)}\approx12.2ℓ=

cos(35)

10

≈12.2

The length of the wooden board is about 12.2 feet.

Step-by-step explanation:

hope it's help