FIRST PARTWe need to find sin α, cos α, and cos β, tan β
α and β is located on third quadrant, sin α, cos α, and sin β, cos β are negative
Determine ratio of ∠α
Use the help of right triangle figure to find the ratio
tan α = 5/12
side in front of the angle/ side adjacent to the angle = 5/12
Draw the figure, see image attached
Using pythagorean theorem, we find the length of the hypotenuse is 13
sin α = side in front of the angle / hypotenuse
sin α = -12/13
cos α = side adjacent to the angle / hypotenuse
cos α = -5/13
Determine ratio of ∠β
sin β = -1/2
sin β = sin 210° (third quadrant)
β = 210°
SECOND PARTSolve the questions
Find sin (α + β)
sin (α + β) = sin α cos β + cos α sin β
Find cos (α - β)
cos (α - β) = cos α cos β + sin α sin β
Find tan (α - β)
Simplify the denominator
Simplify the numerator
Simplify the fraction
Answer:8 I think, sorry it it is wrong
Step-by-step explanation:
AWNSER: $90.75
Shelly earns $90.75 in compound interest after 3 years. All together she has $695.75.
Answer:
what
Step-by-step explanation:
The figure of the prism is attached below.
The total surface area of the prism equals the sum of areas of two triangles and the three rectangles.
Surface Area of Prism = Area of 2 Triangles + Area of 3 Rectangles.Area of a Triangle = 0.5 x Base x Height
Area of a Triangle = 0.5 x 3 x 4 = 6 square units
There are 3 rectangles. From the figure we can see that the bottom most rectangle has the dimensions 4 by 6. The left most rectangle has the dimensions 3 x 6 and the right most rectangle has the dimensions 5 by 6.
So, the Area of 3 rectangles will be = (4 x 6) + (3 x 6) + (5 x 6) = 72 square units
The Surface Area of the prism will be:
Surface Area = 2 (4) + 72 = 84 square units
Thus the correct answer is option A