If sinx =0.6 and AB =12, then area of triangle ABC is equal to 96 units².
As given in the question,
In triangle ABC,
AB = Perpendicular side
BC = Base
AC = Hypotenuse
sinx = 0.6
AB = 12
sinx = AB / AC
⇒0.6 = 12/AC
⇒AC = 12 /0.6
⇒ AC = 20
Using Pythagoras theorem,
AB² + BC² = AC²
⇒ BC² = 20² -12²
⇒BC = 16
Area of ΔABC = (1/2)× AB×BC
= (1/2)×12×16
= 96 units²
Therefore, if sinx =0.6 and AB =12, then area of triangle ABC is equal to 96 units².
The complete question is:
If sin x = 0.6 and AB = 12 as shown in the diagram , what is the area of ΔABC ?
a. 96 units²
b. 28.8 units²
c. 31.2 units²
d. 34.6 units²
e. 42.3 units²
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