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°
Simple, use PEMDAS and then do your simple math and then your answer should be 86922.56604
Answer:
This is the alternate exterior angle theorem
Step-by-step explanation:
This is because angle 2 and angle 7 are in the <u>outer</u> part of each side of opposite lines
5 yellow marbles out of total of 17 marbles so 5/17
Answer:
The expression of h as function of x is h = ![\sqrt{(d + 5500) (d - 5500)}](https://tex.z-dn.net/?f=%5Csqrt%7B%28d%20%2B%205500%29%20%28d%20-%205500%29%7D)
Step-by-step explanation:
Given as :
The distance of blimp (AB) = 5500 feet
The slanted distance to the pagoda (BC) = d feet
The horizontal distance (AC) = h
Let the angle made between slanted distance and horizontal distance be Ф
So , cos Ф =
= ![\frac{h}{d}](https://tex.z-dn.net/?f=%5Cfrac%7Bh%7D%7Bd%7D)
And sin Ф =
= ![\frac{5500}{d}](https://tex.z-dn.net/?f=%5Cfrac%7B5500%7D%7Bd%7D)
∵, cos²Ф = 1 - sin²Ф
So,
= ![1 - (\frac{5500}{d})^{2}](https://tex.z-dn.net/?f=1%20-%20%28%5Cfrac%7B5500%7D%7Bd%7D%29%5E%7B2%7D)
Or,
=
Or, h² = d² - 5500²
∴ h = ![\sqrt{d^{2}- 5500^{2}}](https://tex.z-dn.net/?f=%5Csqrt%7Bd%5E%7B2%7D-%205500%5E%7B2%7D%7D)
Or, h = ![\sqrt{(d + 5500) (d - 5500)}](https://tex.z-dn.net/?f=%5Csqrt%7B%28d%20%2B%205500%29%20%28d%20-%205500%29%7D)
Hence The expression of h as function of x is h =
Answer