Is this college math or high school math
Answer:
a) 10.7 cm
b) 11.6 cm
c) 29.9 cm²
Step-by-step explanation:
a) sin(α)/a = sin(β)/b
sin(∠BCD)/BD = sin(DBC)/DC
sin(41°)/BD = sin(55°)/13.4
BD = 13.4*sin(41°)/sin(55°) = 10.73 cm ≈ 10.7 cm
b) From ΔBCD , ∠BDC = 180-(41+55) = 84°
∠ABD and ∠BDC are alternate interior angles, so they are congruent, and
∠ABD = ∠BDC = 84°
AD²= AB² + BD² - 2*AB*BD*cos (∠ABD) =
= 5.6² + 10.73² - 2*5.6*10.73*cos(84°) = 133.93 cm²
AD =√(133.93) ≈11.6 cm
c) Area(ADB) = (1/2)*AB*BD*sin(∠ABD)=(1/2)*5.6*10.73*sin(84°) ≈ 29.9 cm²
Answer:
The length and width of the rectangle are 20 feet and 31.25 feet, respectively.
Step-by-step explanation:
Let the scale be
and the dimensions of the rectangle being 4 inches and 5 inches, respectively. The scale (
), measured in inches per feet, is equivalent to the following rational number:

We can convert each length by dividing it by scale factor. That is:
Length


Width


The length and width of the rectangle are 20 feet and 31.25 feet, respectively.
Answer:
x = 2, x = -5/2
Step-by-step explanation:
2x² + x - 10 = 0
(2x + 5)(x - 2) = 0
2x + 5 = 0
2x = -5
x = -5/2
x - 2 = 0
x = 2