Answer:
see explanation
Step-by-step explanation:
(a)
sum the parts of the ratio, 3 + 2 + 1 = 6 parts
The sum of the 3 angles in a triangle = 180° , then
180° ÷ 6 = 30° ← value of 1 part of the ratio , then
3 parts = 3 × 30° = 90°
2 parts = 2 × 30° = 60°
1 part = 30°
The angles in the triangle are 90°, 60°, 30°
Thus the triangle is right angled
(b)
The shortest side is opposite the smallest angle, that is opposite 30°
Using the sine ratio in the right triangle and the exact value
sin30° = [tex]\frac{1}{2}[/tex]
sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{opposite}{25}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
2 × opposite = 25 ( divide both sides by 2 )
opposite = 12.5
That is shortest side is 12.5 cm
