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A triangle ABC, AB = 6 cm and AC = 8 cm. It is also known that the sum of angles B & C is 120 degrees. If the angle bisector of the remaining angle meets BC at a point P, then find the length of AP?
- a)24√3/7
- b)24√3/5
- c)20√3/7
- d)20√3/5
Correct answer is option 'A'. Can you explain this answer?
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A triangle ABC, AB = 6 cm and AC = 8 cm. It is also known that the su...
Let us consider AP to be of length 'x' cm, as is shown in the diagram.
Angle A = 60 degrees, since Sum of angles B & C is 120 degrees.
Now since AP is the angle bisector of angle A, hence the sides BP:CP will be in the ratio of 6:8 = 3:4.
Now we know that ar(ABC) = ar(ABP) + ar(ACP)
Using the formula of area(ar) = ½ *a.b. sinC, where C is the angle formed between sides of length a and b, respectively, we get
(1/2 *6*8 sin 60) = (½ * 6*x*sin 30) + ( ½ * 8*x*sin 30)
or 24√3/2 = 3x/2 + 4x/2
or 12√3 = 7x/2
or x = 24√3/7
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A triangle ABC, AB = 6 cm and AC = 8 cm. It is also known that the su...
The sum of the angles in a triangle is always 180 degrees. Therefore, we can write the equation:
angle A + angle B + angle C = 180
Since angle B and angle C are given as supplementary, we can write another equation:
angle B + angle C = 180
We can substitute this equation into the first equation:
angle A + (angle B + angle C) = 180
angle A + 180 = 180
Simplifying this equation, we get:
angle A = 0
However, an angle cannot be 0 degrees in a triangle, so there must be an error in the given information. Please check the question again and provide the correct information.
angle A + angle B + angle C = 180
Since angle B and angle C are given as supplementary, we can write another equation:
angle B + angle C = 180
We can substitute this equation into the first equation:
angle A + (angle B + angle C) = 180
angle A + 180 = 180
Simplifying this equation, we get:
angle A = 0
However, an angle cannot be 0 degrees in a triangle, so there must be an error in the given information. Please check the question again and provide the correct information.
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