Question

unit 1 test a ib applications sl

1. find the value of x.
2. suav wants to use a sheet of fiberboard 27 inches long to create a skateboard ramp with a 19 - degree angle of elevation from the ground. how high will the ramp rise from the ground at its highest end? round your answer to 2 dp.

Explanation:

Step1: Identify trig - function for question 15

In right - triangle \(PQO\), we know the adjacent side to angle \(x\) is \(8.5\) and the hypotenuse is \(18\). We use the cosine function \(\cos(x)=\frac{\text{adjacent}}{\text{hypotenuse}}\). So \(\cos(x)=\frac{8.5}{18}\).

Step2: Solve for \(x\)

\(x = \cos^{- 1}(\frac{8.5}{18})\). Using a calculator, \(x=\cos^{-1}(\frac{8.5}{18})\approx61.81^{\circ}\).

Step3: Identify trig - function for question 16

We have a right - triangle where the hypotenuse \(y = 27\) inches and the angle of elevation is \(19^{\circ}\), and we want to find the opposite side \(x\) (height of the ramp). We use the sine function \(\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}\), so \(\sin(19^{\circ})=\frac{x}{27}\).

Step4: Solve for \(x\)

\(x = 27\times\sin(19^{\circ})\). Using a calculator, \(x = 27\times\sin(19^{\circ})\approx8.78\) inches.

Answer:

1. \(x\approx61.81^{\circ}\)
2. \(x\approx8.78\) inches