Question

Angle A is an acute angle and sin(A) = 11/14. What is the value of cos(A)?

A. 3/14
B. √3/14
C. 5√3/14
D. √(3/14) (2)
What are the values of a and b, if any, where - alb + 4|> 0?
A. a > 0 and b #-4
B. a > 0 and b #4
C. a <0 and b≥-4
D. a <0 and b #-4

Answer 1

To find the value of cos(A), we can use the identity:

sin^2(A) + cos^2(A) = 1

We know that sin(A) = 11/14, so we can substitute this value into the equation and solve for cos(A):

(11/14)^2 + cos^2(A) = 1

121/196 + cos^2(A) = 1

cos^2(A) = 1 - 121/196

cos^2(A) = 75/196

cos(A) = ± √(75/196)

cos(A) = ± (5/14) √3

Since A is an acute angle, cos(A) must be positive. Therefore, the value of cos(A) is:

cos(A) = (5/14) √3

For the second question, we can simplify the inequality:

-alb + 4 > 0

Add alb to both sides:

4 > alb

Divide both sides by b (since b is negative, we must reverse the inequality):

a/b < -4

Therefore, the values of a and b are:

a > 0 and b ≠ 4