Question

1. Find the m

2. Determine the length of side AB.

3. What are the sine and cosine ratios for angles A and B?
sin cos sin cos
4. What do you notice about the sine of angle A and cosine angle B?

5. What do you notice about the cosine of angle A and the sine of angle B?

6. Add up angles A and B. What do they equal?

7. Given the information you obtained in numbers 1-5, determine the kissing angles in A-D below.
a. sin40 degrees=cos
b. cos27 degrees= sin
c. sin90 degrees = cos
d. cos65 degrees = sin

Answer 1

Explanation:

remember, the sum of all angles in a triangle is always 180°.

1. you mean find the angle at A, yes ?

180 = angle A + angle B + angle C =

= angle A + 38 + 90

angle A = 180 - 38 - 90 = 90 - 38 = 52°

2. Pythagoras

AB² = 11² + 8.5² = 121 + 72.25 = 193.25

AB = 13.90143877... in

3. sine/cosine ratio is tangent.

sin(38) × AB = 8.5 in

cos(38) × AB = 11 in

sin(38)/cos(38) = tan(38) = 8.5/11 = 0.772727272...

sin(52) × AB = 11 in

cos(52) × AB = 8.5 in

sin(52)/cos(52) = tan(52) = 11/8.5 = 1.294117647...

4. they are equal. as sin(x) = cos(90-x).

5. they are equal. as cos(x) = sin(90-x).

6. 90°. again, the sum of all angles must be 180°. so, when one angle is all by itself already 90°, then there are only 90° left for the other 2 angles.

7. not sure what you mean by "kissing angles" but

a. sin(40°) = cos(90-40) = cos(50°) = 0.64278761...

b. cos(27°) = sin(90-27) = sin(63°) = 0.891006524...

c. sin(90°) = cos(90-90) = cos(0°) = 1

d. cos(65°) = sin(90 - 65) = sin(25°) = 0.422618262...