Question

ACB is an angle in the semicircle of diameter AB = 5 and AC:BC =3:4 The area of the triangle ABC is​

Answer 1

Answer:

90

Step-by-step explanation:

AB=5

AC=3

BC=4

ABC=90°

Answer 2

Answer:

Area of Triangle = 6

Step-by-step explanation:

In the question,

We have the diameter of circle, AB = 5

Also,

ACB is an angle in the semi-circle.

Now, we know that angle in a semi-circle is a right angle.

So,

Triangle ACB is a right angle with right angle at C.

Also,

AC:BC = 3:4

So,

AC = 3x

BC = 4x

So,

Using the Pythagoras theorem in the triangle we get,

$AB^{2}=AC^{2}+BC^{2}\\25=(3x)^{2}+(4x)^{2}\\16x^{2}+9x^{2}=25\\x^{2}=1\\x=1$

SO,

AC = 3

BC = 4

Now,

Area of the triangle is given by,

$A=\frac{1}{2}\times base\times height\\A=\frac{1}{2}\times AC\times BC\\A=\frac{1}{2}\times 3\times 4=6\\A=6$

Therefore, the Area of the triangle ABC is 6.