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4 years ago

If two angles are supplementary and one angle measures 47°, what is the measure of the other angle?

Mathematics

1 answer:

lara31 [8.8K]4 years ago

5 0

Answer:

133°

Step-by-step explanation:

Supplementary angles add to 180 degrees. Call the unknown angle x

47 +x = 180

Subtract 47 from each side

47-47+x =180-47

x = 133

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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.

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

The possible question options are;

John measures the the distance between the two stakes

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

John multiplies the distance between the two stakes by 1.7 to find the distance

John drives a second stake in the ground

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

John drives a stake opposite the tree to establish a line between two points.

Learn more about trigonometric ratios here:

brainly.com/question/13276558

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3 years ago

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At the time the cannonball reaches the ground, the vertical height of the cannonball from the ground is 0, i.e. h = 0.

Thus, the time it will take the cannonball to reach the ground is given by

$-16t^2+128t=0 \\ \\ \Rightarrow t(-16t+128)=0 \\ \\ \Rightarrow t=0\ or\ -16t+128=0 \\ \\ \Rightarrow16t=128 \\ \\ \Rightarrow t= \frac{128}{16} =8$

Therefore, it will take the cannonball 8 seconds to reach the ground.

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4 years ago

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bixtya [17]

Answer:

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Step-by-step explanation:

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