Question

if the measure of angles of a triangle are proportional to 4, 5 and 6 then measure of the smallest angle of the triangle will be​

Answer 1

Step-by-step explanation:

Let the angles be 4x,6x and 5x

4x+6x+5x=180 ∘

15x=180 ∘

⇒x=12 ∘

So the angles are

4×12 ∘ =48 ∘

5×12 ∘ =60 ∘

6×12 ∘ =72 ∘

Answer 2

Answer:

48°

Step-by-step explanation:

sides of the triangle have a ratio of 4:5:6. So,

Let us first assign the following:

a=4 , b=5 , and c=6

since side a has the shortest side, therefore the angle opposite a (which we will assign as ∠α ) is the smallest angle.

To compute this..we can use the law of cosines.

ie,

a2=b2+c2–2bccos(α)

2bccos(α)=b2+c2−a2

cos(α)=b2+cc−a22bc

Substituting these values, we get

cos(α)=52+62–422(5⋅6)

cos(α)=25+36–1660

cos(α)=4560

cos(α)=34 or 0.75

arccos(0.75)=α we get the measurement of ∠α as ≈ 41.41∘

Otherwise, if the angles of the triangle have a ratio of 4:5:6 , then the smallest angle would have a measure of 48∘