Question

101) Nate built a skateboard ramp that covers a horizontal distance of 10 ft.The ramp rises a total of 3.5 ft. What angle does the ramp make with theground? Round to the nearest degree. *Your answerO This is a Please fill out this field.

Answer 1

The answers to the trigonometry questions are 19.29° and 1642 feets

1.)

Using trigonometric concept;

• Tan(θ) = opposite / Adjacent

Tan(θ) = 3.5/10

Tan(θ) = 0.35

θ = 19.29°

2.)

Using trigonometric concept;

• Tan(θ) = opposite / Adjacent

• The Adjacent = 910
• Opposite = horizontal distance

Substituting into our equation:

Tan(61°) = horizontal distance/ 910

Horizontal distance = 910 × Tan(61°) ≈ 1641.68 feets

Hence, the horizontal distance is 1642 feets

Answer 2

1) The diagram to represent the information is shown below:

To obtain the angle theta, we are going to use the trigonometry ratio to solve this.

The sides provided from the image above are the adjacent side, which is 10ft, and the opposite side, which is 3.5ft. The suitable trigonometry ratio to use is the Tangent.

Thus;

`\begin{gathered} \text{Tan}\theta=\frac{opposite}{\text{adjacent}} \\ \text{Tan}\theta=(3.5)/(10) \\ \text{Tan}\theta=0.35 \\ \theta=\arctan (0.35)=tan^(-1)(0.35) \\ \theta=19.29^0 \\ \theta=19^0\text{ ( to the nearest degree)} \end{gathered}`

Hence, the angle the ramp makes with the ground is 19 degrees

2) The diagrammatic representation of the problem is shown below:

The horizontal distance from the base of the sky-scrapper to the tour bus has been represented as x.

We are going to use the trigonometry ratio to solve for 'x'. The sides provided from the image above are the opposite side, which is x, and the adjacent side, which is 61 degrees. The suitable trigonometry ratio for this case is the Tangent.

Thus, we have:

`\begin{gathered} \text{Tan}\theta=\frac{opposite}{\text{adjacent}} \\ \text{Tan}61=(x)/(910) \\ x=910\text{ x Tan61} \\ x=910\text{ x 1.804} \\ x=1641.68ft \\ x=1642ft\text{ (To the nearest f}eet) \end{gathered}`

Hence, the distance from the base of the sky-scrapper to the tour bus is 1642ft