Question

The angles in a triangle are in the ratio 3:2:1.

Answer 1

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° = $\frac{1}{2}$

sin30° = $\frac{opposite}{hypotenuse}$ = $\frac{opposite}{25}$ = $\frac{1}{2}$ ( cross- multiply )

2 × opposite = 25 ( divide both sides by 2 )

opposite = 12.5

That is shortest side is 12.5 cm