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3 years ago

14

Which set of dimensions is possible for a rectangular prism with volume 420 cm3? A. 4 cm by 8 cm by 12 cm B. 4 cm by 10 cm by 12

cm C. 5 cm by 7 cm by 12 cm D. 5 cm by 8 cm by 12 cm

1 answer:

Ilya [14]3 years ago

3 0

With process of elmination the answer is C because all the rest are the same number but placed it is different order.
~JZ

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Answer:

Part 5) The length of the ski lift is $1.15\ miles$

Part 6) The height of the tree is 18.12 m

Step-by-step explanation:

Part 5)

Let

A -----> Beginning of the ski lift

B -----> Top of the mountain

C -----> Base of mountain

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Par 6)

see the attached figure with letters to better understand the problem

<u><em>Applying the law of sines in the right triangle BDC</em></u>

In the right triangle BDC 20 degrees is the complement of 70 degrees

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<u><em>Applying the law of sines in the right triangle ABC</em></u>

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$BC=(sin(40\°))\frac{x+15}{sin(50\°)}$ -----> equation B

Equate equation A and equation B and solve for x

$(sin(70\°))\frac{x}{sin(20\°)}=(sin(40\°))\frac{x+15}{sin(50\°)}\\\\2.7475x=0.8391(x+15)\\\\2.7475x=0.8391x+12.5865\\\\2.7475x-0.8391x=12.5865\\\\x=6.60\ m$

<u><em>Find the value of BC</em></u>

$BC=(sin(70\°))\frac{6.6}{sin(20\°)}$

$BC=18.12\ m$

therefore

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