Question

a toddlers playground has two slides on either side. the slide on the left is situated at a 45° angle to the ground and is 68 centimeters away from the base of the playground. the sl the ground and is 112 centimeters away from the playgrounds base. what is the total length of both slides on this playground, rounded to the nearest tenth of a centimeter? 96.2 129.3 197.3 225.5

Explanation:

Step1: Calculate the length of the left - hand slide

Use the cosine formula \( \cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}} \). For the left - hand slide with \( \theta = 45^{\circ} \) and adjacent side \( a = 68\) cm.
Since \( \cos45^{\circ}=\frac{\sqrt{2}}{2}\approx0.707\), and \( \cos45^{\circ}=\frac{68}{l_1}\), then \( l_1=\frac{68}{\cos45^{\circ}}=\frac{68}{0.707}\approx96.2\) cm.

Step2: Calculate the length of the right - hand slide

Use the cosine formula \( \cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}} \). For the right - hand slide with \( \theta = 30^{\circ}\) and adjacent side \( a = 112\) cm.
Since \( \cos30^{\circ}=\frac{\sqrt{3}}{2}\approx0.866\), and \( \cos30^{\circ}=\frac{112}{l_2}\), then \( l_2=\frac{112}{\cos30^{\circ}}=\frac{112}{0.866}\approx129.3\) cm.

Step3: Calculate the total length of the two slides

The total length \( L=l_1 + l_2\).
\( L=96.2+129.3 = 225.5\) cm.

Answer:

225.5