What dimensions of the box are required to fit the candle? 5 by 6 by 18 7 by 6 by 18 5 by 3 by 18 7 by 3 by 18

Mathematics

1 answer:

LiRa [457]3 years ago

4 0

The minimum height of the box must be 18 units, which is present in all the choices.
Another minimum dimension that we already know is 7 units, since it is an oblique box, and the projection of bottom-left to top-right is shown as 7 units.
That leaves us with the second (7x6) or fourth choice (7x3).

We have not been given the other dimension of the triangle, but from common sense, it looks longer than the front (5 units) leg, therefore 6 units is not an unreasonable dimension.

With 99.5% certainty, I would choose the second choice (7x6x18) because the remaining dimension does not look like 3 units long.

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John wants to measure the width of a stream using the methods he has learned in geometry. He puts a stake in the ground opposite

otez555 [7]

John's method to determine the width of the stream uses the knowledge

that the tangent of 60° is approximately 1.7.

The proper sequence John would use to find the width of the stream are;

Step 1; John drives a stake opposite the tree to establish a line between two points

Step 2; John uses a compass to walk away from the stakes at a right angle

Step 3; On the path John walks until he finds a line of sight to the tree that equals 60 degrees

Step 4; John drives a second stake in the ground

Step 5; John measures the the distance between the two stakes

Step 6; John multiplies the distance between the two stakes by 1.7 to find the distance.

Reasons:

The steps that can be used to measure the width of the stream are;

Step 1: Drive a stake opposite the tree on the other side of the stream.

Step 2: With the aid of a compass, walk at right angles to the line formed by the stake and the tree.

Step 3; Keep walking along the previous path till a point is reached where the angle formed between the line of site to the tree and the walk path is 60°.

Step 4; At the point where the line of sight to the tree is 60°, a second stake is driven in the ground.

Step 5; Measure the distance between the stakes that are placed in the ground.

Step 6; Given that by trigonometry, the ratio of the width of the stream to the distance between the two stakes is tan(60°) ≈ 1.7, multiply the distance between the two stakes by 1.7 to find the width of the stream.

$\displaystyle tan(60^{\circ}) = \mathbf{\frac{Width \ of \ stream}{Distance \ between \ stakes}}$