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Brut [27]
3 years ago
9

Michel is building an in-ground swimming pool. it has a length of 16 feet, a width of 10 feet, and a depth of 8 feet. How many c

ubic feet of water will the pool if the pool is completely?
PLEASE SHOW YOUR WORK


10 PIONTS!!!
Mathematics
1 answer:
jonny [76]3 years ago
4 0
The swimming pool is a <span>rectangular prism</span> (which means it's a 3D rectangle). To find the volume of a rectangular prism you multiply Length x Width x Height.

In this case that would mean 16*10*8 (height and depth are the same in this problem).

16*10*8=<span>1280 ft</span>³<span>
</span>
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A surveyor sights the far bank of a river at an angle of 110° to the near bank. She then moves 75 feet upriver and sights the sa
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Answer:

Correct answer is 54.82 ft.

Step-by-step explanation:

First of all, let us label the diagram and do the construction as per the attached answer image.

Let us consider \triangle ABC:

\angle B = 90^\circ\\\angle ACB = 180-110 = 70^\circ

Let side AB = d ft and let side BC = x ft

We need to find AB to find the shortest distance across the river.

Using trigonometric identity of tangent:

tan\theta = \dfrac{Perpendicular}{Base}

tan 70 = \dfrac{d}{x}\\\Rightarrow x = \dfrac{d}{tan70} = 0.36d ..... (1)

Now, let us have a look at another right angled triangle ABD:

Let us consider \triangle ABC:

\angle B = 90^\circ\\\angle ADB = 180-150 = 30^\circ

side AB = d ft and side BD = x+75 ft

Using trigonometric identity of tangent:

tan\theta = \dfrac{Perpendicular}{Base}

tan 30 = \dfrac{d}{x+75}\\\text{Using equation (1)}:\\0.577 = \dfrac{d}{0.36d+75}\\\Rightarrow 0.207d + 43.27 = d\\\Rightarrow 0.793d = 43.27\\\Rightarrow d \approx 54.82\ ft

Correct answer is 54.82 ft.

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