Answer: The correct option is (a), i.e., cos B= sin A.
Explanation:
It is given that the ∠B = ∠C and ∠D is a right angle.
Since two corresponding angles of both triangles are same, so by angel sum property three angles are also equal. Therefore by AAA rule both triangles are similar.
It is given that,
Using angle sum property angle C is written as,
By using quadrant concepts.
Therefore option A is correct.
Answer:
Not teenagers = 1120
Step-by-step explanation:
Total number of audience members = 1600
30% of the audience were teenagers.
It means 70% of the audience were not teenagers. It can be given by :
x = 70% of 1600
Hence, 1120 audiences were not teenagers.
From the setup of the problem, the "length of the top of the bookcase, measured along the attic ceiling" will be the hypotenuse of a right triangle, the length "AB". We have both the angle between AB and AC and the length of AC (3.24 meters), so we can use trigonometric identities.
The cosine of the 40 degree angle between AB and AC is equivalent to the length of AC divided by the length of AB. Equivalently, we have:
where "h", the hypotenuse, is the length we want. Rearranging the formula to solve for h we have that
which is 4.2295... meters. Converting to centimeters (multiplying by 100) we have that h = 422.95... centimeters, or if we round the value, h = 423 centimeters.