Exercise 1 Page 583

We are given that Lenora wants to build a bike ramp, and we're asked to find the length of the base of this ramp. Let $ℓ$ represents this length. We will focus on the side wall, which is a right triangle.

Since we are given that the angle of elevation is

2 0^{\circ},

we can use one of the trigonometric ratios to evaluate the value of

ℓ .

Let's recall that the tangent of

∠ A

is the ratio of the leg opposite

∠ A

to the leg adjacent

∠ A .

Using this definition, we can create an equation for

tan 2 0^{\circ} .

tan 2 0^{\circ} = \frac{1 0}{ℓ}

Let's solve the above equation.

tan 2 0^{\circ} = \frac{1 0}{ℓ}

MultEqn

$LHS \cdot ℓ = RHS \cdot ℓ$

ℓ tan 2 0^{\circ} = 10

DivEqn

$LHS / tan 2 0^{\circ} = RHS / tan 2 0^{\circ}$

ℓ = \frac{1 0}{tan 2 0 ^{\circ}}

UseCalc

Use a calculator

ℓ = 27.47477 \dots

RoundDec

Round to $1$ decimal place(s)

ℓ \approx 27.5

The length of the base of the ramp is approximately

27.5

feet.