Question

Sinb= 5/13 и угол б тупой. найдите его косинус

Answer 1

Решение:
1)Т. к. угол В-тупой, значит, его косинус меньше нуля.
cosB=-V(1-sin²B);cosB=-V(1-25/169)=-V144/169=-12/13.
2)Применим т. косинусов:
AC²=AB²+BC²-2AB*BC*cosB
AC²=13²+2²-2*13*2*(-12/13)
AC²=169+4+48
AC²=221
AC=V221

Answer 2

To find the cosine of angle B, we can use the given value of the sine of angle B and the fact that angle B is obtuse (which means its cosine will be negative). Here's the step-by-step solution:

Given: Sin(B) = 5/13 Angle B is obtuse.

We know that for any angle A, the following trigonometric identity holds: sin^2(A) + cos^2(A) = 1

Let's use this identity to find the cosine of angle B: cos^2(B) = 1 - sin^2(B)

Now, substitute the value of sin(B): cos^2(B) = 1 - (5/13)^2 cos^2(B) = 1 - 25/169 cos^2(B) = (169/169) - (25/169) cos^2(B) = 144/169

Now, take the square root of both sides to find the cosine of angle B (remembering that it's negative because it's obtuse):

cos(B) = -√(144/169) cos(B) = -12/13

So, the cosine of angle B is -12/13.