Answer: BC = 5.83
Step-by-step explanation:
Luckily, the triangle is placed on the graph nicely so we can count the legs of the triangle:
AB = 5
AC = 3
BC = ?
To find BC, we can simply use the Pythagorean Theorem:
![a^{2}+b^{2}=c^{2}](https://tex.z-dn.net/?f=a%5E%7B2%7D%2Bb%5E%7B2%7D%3Dc%5E%7B2%7D)
5^2 + 3^2 = c^2
25 + 9 = c^2
34 = c^2
Now square root to find c, or BC.
![\sqrt{34}=\sqrt{c^{2} }](https://tex.z-dn.net/?f=%5Csqrt%7B34%7D%3D%5Csqrt%7Bc%5E%7B2%7D%20%7D)
c = 5.83 (rounded by nearest hundredth)
36 Multiplication tables are:
36
72
108
Therefore we must know that the whole number is 72, but we need to find out how many times it goes into 100 so:
100-72=28.
Therefore it goes in 2 28/32 times, which can be simplified to 2 7/8
Answer:
<em>The angle of elevation of the sun is 32°</em>
Step-by-step explanation:
<u>Right Triangles</u>
The flagpole and the ground form a right angle (90°). In triangles with right angles, the trigonometric ratios are satisfied.
Each acute angle has an adjacent leg and an opposite leg. The tangent ratio relates to both legs.
![\displaystyle \tan x=\frac{\text{opposite leg}}{\text{adjacent leg}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Ctan%20x%3D%5Cfrac%7B%5Ctext%7Bopposite%20leg%7D%7D%7B%5Ctext%7Badjacent%20leg%7D%7D)
The opposite leg to angle x is 20 ft and the adjacent leg is 32 ft, thus:
![\displaystyle \tan x=\frac{20}{32}=0.625](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Ctan%20x%3D%5Cfrac%7B20%7D%7B32%7D%3D0.625)
Calculate x by using the inverse tangent:
![x=\arctan 0.625](https://tex.z-dn.net/?f=x%3D%5Carctan%200.625)
![x=32^\circ](https://tex.z-dn.net/?f=x%3D32%5E%5Ccirc)
The angle of elevation of the sun is 32°
Answer:
f(x) = 16*(3/2)^(x-1)
Step-by-step explanation:
See attachment.