Answer:
10 ft to nearest foot.
Step-by-step explanation:
We use the Pythagoras theorem:
12^2 = 6^2 + h^2 where h is the height on the barn
h^2 = 12^2 - 6^2
h^2 = 144 - 36 = 102
h= √108 = 10.39
Answer:
D) 3768 inches
Step-by-step explanation:
Given,
No. of plates = 100
Diameter of each plate = 12inches
So, radius of each plate = 12 / 2 = 6 inches
So, circumference of each plate
![= 2\pi \: r](https://tex.z-dn.net/?f=%20%3D%202%5Cpi%20%5C%3A%20r)
= 2 × 3.14 × 6 inches
= 37.68 inches
Hence, circumference of 100 plates = 100 × 37.68 inches
= 3768 inches
Hence, <u>3768 inches</u> of gold trim is required (Ans)
Step-by-step explanation:
![i) \: \frac{3}{5} \times ( \frac{ - 7}{8} ) = - \frac{21}{40} \\ \\ ii) \: \frac{ - 9}{2} \times \frac{5}{4} = - \frac{45}{8} \\ \\ iii) \: \frac{ - 6}{11} \times \frac{5}{3} = - \frac{10}{11} \\ \\ iv) \: \frac{ - 2}{3} \times \frac{6}{7} = - \frac{4}{7} \\](https://tex.z-dn.net/?f=i%29%20%5C%3A%20%20%5Cfrac%7B3%7D%7B5%7D%20%20%5Ctimes%20%28%20%20%20%5Cfrac%7B%20-%207%7D%7B8%7D%20%29%20%3D%20%20-%20%20%5Cfrac%7B21%7D%7B40%7D%20%20%5C%5C%20%20%5C%5C%20ii%29%20%5C%3A%20%20%5Cfrac%7B%20-%209%7D%7B2%7D%20%20%5Ctimes%20%20%5Cfrac%7B5%7D%7B4%7D%20%20%3D%20%20%20-%20%5Cfrac%7B45%7D%7B8%7D%20%20%5C%5C%20%20%5C%5C%20iii%29%20%5C%3A%20%20%5Cfrac%7B%20-%206%7D%7B11%7D%20%20%5Ctimes%20%20%5Cfrac%7B5%7D%7B3%7D%20%20%3D%20%20-%20%20%5Cfrac%7B10%7D%7B11%7D%20%20%5C%5C%20%20%5C%5C%20iv%29%20%5C%3A%20%20%5Cfrac%7B%20-%202%7D%7B3%7D%20%20%20%5Ctimes%20%20%5Cfrac%7B6%7D%7B7%7D%20%20%3D%20%20-%20%20%5Cfrac%7B4%7D%7B7%7D%20%20%5C%5C%20)
Answer:
<em>The height of the bullding is 717 ft</em>
Step-by-step explanation:
<u>Right Triangles</u>
The trigonometric ratios (sine, cosine, tangent, etc.) are defined as relations between the triangle's side lengths.
The tangent ratio for an internal angle A is:
![\displaystyle \tan A=\frac{\text{opposite leg}}{\text{adjacent leg}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Ctan%20A%3D%5Cfrac%7B%5Ctext%7Bopposite%20leg%7D%7D%7B%5Ctext%7Badjacent%20leg%7D%7D)
The image below shows the situation where Ms. M wanted to estimate the height of the Republic Plaza building in downtown Denver.
The angle A is given by his phone's app as A= 82° and the distance from her location and the building is 100 ft. The angle formed by the building and the ground is 90°, thus the tangent ratio must be satisfied. The distance h is the opposite leg to angle A and 100 ft is the adjacent leg, thus:
![\displaystyle \tan 82^\circ=\frac{h}{100}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Ctan%2082%5E%5Ccirc%3D%5Cfrac%7Bh%7D%7B100%7D)
Solving for h:
![h = 100\tan 82^\circ](https://tex.z-dn.net/?f=h%20%3D%20100%5Ctan%2082%5E%5Ccirc)
Computing:
h = 711.5 ft
We must add the height of Ms, M's eyes. The height of the building is
711.5 ft + 5 ft = 716.5 ft
The height of the building is 717 ft
The answer to your problem is that Marisol’s shadow would be 144 feet long