Question

17. In a right ,∆ABC, AC is the hypotenuse of length 10cm. If <A = 30°, then the area of the
triangle is
A) (25 V 3)/3 sq.cm.
B) (25 V 3)/2 sq.cm.
C) 25 V 3 sq.cm.
D) 25sq. cm​

Answer 1

Answer. D 25sq. cm is answer

Answer 2

The area of the triangle is (25 V 3)/2 sq.cm. The answer is option B) (25 V 3)/2 sq.cm.

Since ∆ABC is a right triangle, we can use trigonometric ratios to find the length of the other sides.

Let's call the length of side AB "a" and the length of side BC "b". Then we have:

sin 30° = AB/10 (using opposite/hypotenuse ratio in a right triangle)

=> AB = 10(sin 30°) = 5 cm

cos 30° = BC/10 (using adjacent/hypotenuse ratio in a right triangle)

=> BC = 10(cos 30°) = 5√3 cm

Now we can use the formula for the area of a triangle, which is:

Area = (1/2) x base x height

Since ∆ABC is a right triangle, we can take AB as the base and BC as the height. So we have:

Area = (1/2) x AB x BC

=> Area = (1/2) x 5 x 5√3

=> Area = (25√3)/2 sq.cm.

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