Answer:
≈ 5.2 ft
Step-by-step explanation:
sum the parts of the ratio, 3 + 1 + 5 = 9 parts
Divide the angle sum of a triangle by 9 to find the value of one part of the ratio.
180° ÷ 9 = 20° ← value of 1 part of the ratio, then
3 parts = 3 × 20° = 60°
5 parts = 5 × 20° = 100°
The angles of the triangle are 100°, 60° and 20°
The longest side is opposite the largest angle in the triangle
The shortest side is opposite the smallest angle in the triangle.
Thus
the longest side is opposite 100°
the shortest side is opposite 20°
let x represent the shortest side and using the Sine rule
[tex]\frac{x}{sin20}[/tex] = [tex]\frac{15}{sin100}[/tex] ( cross- multiply )
x × sin100° = 15sin20° ( divide both sides by sin100° )
x = [tex]\frac{15sin20}{sin100}[/tex] ≈ 5.2 ( to the nearest tenth )
Thus the shortest side is ≈ 5.2 ft
