Question

Can someone help me with this question please !

Answer 1

see explanation

Explanation:

(a)

Sum the parts of the ratio, 1 + 2 + 3 = 6 parts

Divide 180° ( sum of angles in a triangle ) by 6 to find the value of one part of the ratio.

180° ÷ 6 = 30° ← value of 1 part of the ratio, thus

2 parts = 2 × 30° = 60°

3 parts = 3 × 30° = 90°

Thus the triangle is right

-----------------------------------------

(b)

The sides of a 90°- 60°- 30° triangle are in the ratio

2 -
`√(3)` - 1 ( where 2 represents the hypotenuse )

Thus the other 2 sides of the triangle are

19 ÷ 2 = 9.5 , and

9.5 ×
`√(3)` ≈ 16.45

The shortest side is 9.5

Answer 2

a) A triangle which the angles ratio is 1 : 2 : 3 is a 30º - 60º - 90º right triangle.

b) The shortest side is opposite to the shortest angle. So, we can calculate it using sin 30º.

`$\text{sin}(30\º)=\frac{\text{Opposite side to x}}{19} $`

`$(1)/(2) =\frac{\text{Opposite side to x}}{19} $`

`$\text{Opposite side to x}= 9.5$`