Answer:
Height of the lamppost = 5.602 ft + 2.912 ft = 8.514 ft
Step-by-step explanation:
The illustration form a triangle that can be demarcated into 2 right angle triangle. One triangle representing depression triangle and the other elevation triangle.
Depression triangle
The opposite side of the triangle formed is the length of the pole from the base to the horizontal line of sight. Therefore,
using tangential ratio
tan 35° = opposite/adjacent
tan 35° = a/8
cross multiply
a = 8 tan 35°
a = 8 × 0.70020753821
a = 5.60166030568
a = 5.602 ft
Elevation triangle
The opposite side of this right angle triangle represent the length from the horizontal line of sight to the top of the lamppost.
tan 20° = opposite/adjacent
tan 20° = b/8
cross multiply
b = 8 tan 20°
b = 8 × 0.36397023426
b = 2.91176187413
b = 2.912 ft
Height of the lamppost = 5.602 ft + 2.912 ft = 8.514 ft
0.8 inches
the volume (V) of a sphere is calculated using the formula
V = πr³
change the subject and express in terms of r
multiply both sides by 3
3V = 4πr³ ( divide both sides by 4π )
r³ = 3V / 4π ( take the cube root of both sides )
r = ∛( 3V /4π )
sphere A with V= 40
r = ∛ (120 / 12.56 ) = 2.122
sphere B with V = 10
r = ∛(30 / 12.56 ) = 1.337
sphere A - sphere B = 2.122 - 1.337 = 0.8 inches ( to nearest tenth )
Answer:
2^5 × 7
Step-by-step explanation:
Since there is no picture shown, I just plotted the given data points myself. That is shown in the attached picture. The blue rectangle is rectangle PQRS while the orange one is rectangle JKLM. I believe there are some choices for this question but you forgot to include. Nevertheless, I will give my observations from the given figure.
The tile PQRS is bigger than tile JKLM. A rectangle is a two-dimensional shape that has two sets of equal parallel planes. Thus, its area is equal to the length multiplied by its width.
tile PQRS = (9-5)*(12-7) = 20 units²
tile JKLM = (6-4)*(10-5) = 10 units²
Tile PQRS is larger by 10 units².
Answer:
177.7
Step-by-step explanation:
not good with steps