It is known that the sine of an angle in a right-angled triangle is equal to the ratio of the opposite leg to the hypotenuse.
By condition, sin A = 0.4 and the adjacent leg AC = 3 (21) ^ 0.5 are given in a right-angled triangle ABC.
You can calculate the cosine of angle A using the trigonometric identity
(cos A) ^ 2 + (sin A) ^ 2 = 1.
Where, (1 – (sin A) ^ 2) ^ 0.5;
cos A = (1 – 0.4 ^ 2) ^ 0.5 = 0.4 (21) ^ 0.5.
On the other hand, cos A = AC / AB and
the hypotenuse is equal to AB = AC / cos A;
AB = 3 (21) ^ 0.5 / 0.4 (21) ^ 0.5 = 7.5.
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