the figure AB = 11cm, BC = 8cm, AD = 3cm, AC = 5cm and DAC is a right angle.
The size of ADC;
The size of ACB;
The area of the quadrilateral ABCD.
tan ADC = 5/3
11^2 = 5^2+8^2 - 2*5*8 cos ACB
Now you can figure the areas of the triangles ACD and ACB, and just add them up for the area of ABCD
DAC = 1/2(AD)(AC)
So area ACB =1/2(AB)(BC)sin(ACB)
You just repeated the solution Steve gave you here:
https://www.jiskha.com/questions/1765464/In-the-figure-AB-11cm-BC-8cm-AD-3cm-AC-5cm-and-DAC-is-a-right-angle-The
I don't understand why you re-posted the question.
Just do what he told you to do.
Try to explain .. homework please
To find the size of ADC, we can use the fact that DAC is a right angle. Since DAC is a right angle and the lengths of AD and AC are given, we can use the tangent function to find the size of ADC. The tangent of ADC is equal to the ratio of the length opposite to ADC (which is 5 cm) to the length adjacent to ADC (which is 3 cm). So, we have:
tan(ADC) = 5/3
To find the size of ACB, we can use the Law of Cosines. The Law of Cosines states that in a triangle with side lengths a, b, and c, and opposite angles A, B, and C respectively, the following equation holds:
c^2 = a^2 + b^2 - 2ab * cos(C)
In this case, we have:
AB = 11 cm
BC = 8 cm
AC = 5 cm
The angle ACB is opposite to side AB. So, if we substitute the values into the Law of Cosines equation, we can solve for the angle ACB:
11^2 = 5^2 + 8^2 - 2 * 5 * 8 * cos(ACB)
Simplifying this equation will give us the value of cos(ACB), and then we can find the size of ACB by taking the inverse cosine (or arc cosine) of this value.
To find the area of the quadrilateral ABCD, we can divide it into two triangles, ACD and ACB. The area of a triangle can be found using the formula: Area = 1/2 * base * height. In this case, the base of triangle ACD is AD and the height is AC. The base of triangle ACB is AB and the height is BC. We can calculate the areas of both triangles and add them together to get the area of the quadrilateral ABCD.
Finally, to find the area of ACB, we can use another formula for the area of a triangle, which is: Area = 1/2 * base * height * sin(angle). Since we know the base (AB) and the height (BC) of triangle ACB, we need to find the sin(ACB) to calculate its area.