In triangle ABC, angle C is 90 °. tgA = √51 / 7. Find sinB.
| July 6, 2021 | education
The tangent of the angle of a right-angled triangle is the ratio of the opposite leg to the adjacent one, then:
tgBAC = BC / AC = √51 / 7.
Let the length of the segment AC = 7 * X cm, then the length of the leg BC = √51 cm.
We apply the Pythagorean theorem and determine the length of the hypotenuse AB.
AB ^ 2 = AC ^ 2 + BC ^ 2 = 49 * X ^ 2 + 51 * X ^ 2 = 100 * X ^ 2.
AB = 10 * X cm.
Determine the sine of the angle ABC of a right-angled triangle ABC,
SinABS = AC / AB = 7 * X / 10 * X = 7/10 = 0.7.
Answer: The sine of angle B is 0.7.
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