In triangle ABC: angle C = 90 degrees, AC = 6, sin = 0.6. Push the length of the BC side.
| May 11, 2021 | education
If a triangle has an angle of 90, then this triangle is right-angled.
It is known that the sine of an acute angle in a right-angled triangle is the ratio of the opposite leg to the hypotenuse:
sin B = AC: AB.
6/10 = 6: x.
x = 6 * 10: 6.
x = 10 cm.
AB = 10 cm.
According to the Pythagorean theorem, in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.
c ^ 2 = a ^ 2 + b ^ 2.
AB ^ 2 = AC ^ 2 + CB ^ 2.
CB ^ 2 = AB ^ 2 – AC ^ 2
CB ^ 2 = 10 x 10 – 6 x 6 = 100 – 36 = 64.
CB = √64 = 8.
Answer: CB is 8 cm.
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