The angles of a triangle are in the ratio
3:7: 8
Then the greater angle in radions
Answers
Answer:
The ratio of angles of triangles are 3:7:8
Let the measures of triangles are 3x,7x,8x.
⇒ 3x+7x+8x=180
o
[ Sum of angles of triangle is 180
o
]
⇒ 18x=180
o
⇒ x=
18
180
o
=10
o
⇒ 3x=3×10
o
=30
o
⇒ 7x=7×10
o
=70
o
⇒ 8x=8×10
o
=80
o
∴ Greatest and the smallest angles are 80
o
and 30
o
.
Solution:
Since the angles of triangle are in the ratio 3:7:8, let us consider the sides to be
- ∠A = 3x
- ∠B = 7x and
- ∠C = 8x
By Angle Sum Property, the sum of all angles in any triangle is always 180°
∠A + ∠B + ∠C = 180°
➟ 3x + 7x + 8x = 180°
⇒ 10x + 8x = 180°
⤏ 18x = 180°
⤏ x = 180° ÷ 18
⤇ x = 10°
Now for finding the angles of greatest angle;
As we already know that 8x is the greatest angle,
substitute the value of x.
8x
= 8 (10)
= 80°
For converting into radians:
Radians measure = (Degree measure ÷ 180) π
➝ Radians measure = (80 ÷ 180) π
➝ Radians measure = (4 ÷ 9) π
∴ Radians measure of greatest angle = 4π/9