Question

1. priya is teaching her younger cousin to ride a bike. she wants to stay on roads that are not too steep and easy enough for a new bike rider. she has decided the roads must have an angle less than or equal to 7 degrees. a 7 degree angle in a right triangle has a 3:25 ratio for the legs. select the legs of all right triangles that would be safe for a new bike rider. 650 cm, 1000 cm 7 yds, 35 yds 3 m, 25 m 9 units, 72 units 6 ft, 50 ft

Explanation:

Step1: Calculate the ratio for each option

For a right - triangle, if the legs are \(a\) and \(b\) (\(a\) is the opposite side and \(b\) is the adjacent side for the angle in question), we use the formula \(\tan\theta=\frac{a}{b}\). We want \(\frac{a}{b}\leq\frac{3}{25}= 0.12\)

Option1: \(a = 650\mathrm{cm},b = 1000\mathrm{cm}\)

\(\frac{a}{b}=\frac{650}{1000}=0.65>0.12\)

Option2: \(a = 7\mathrm{yds},b = 35\mathrm{yds}\)

\(\frac{a}{b}=\frac{7}{35}=\frac{1}{5}=0.2>0.12\)

Option3: \(a = 3\mathrm{m},b = 25\mathrm{m}\)

\(\frac{a}{b}=\frac{3}{25}=0.12\)

Option4: \(a = 9\mathrm{units},b = 72\mathrm{units}\)

\(\frac{a}{b}=\frac{9}{72}=\frac{1}{8}=0.125>0.12\)

Option5: \(a = 6\mathrm{ft},b = 50\mathrm{ft}\)

\(\frac{a}{b}=\frac{6}{50}=0.12\)

Answer:

3 m, 25 m; 6 ft, 50 ft