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3 years ago

The ratio of two complementary angles is 5 to 1. what are the angles?

1 answer:

6 0

Call x and y those angles. If they are complementary, then their sum equals 90°:

x + y = 90°

y = 90° - x

The ratio of them is 5 to 1. So,

x/y = 5/1

x/(90° - x) = 5/1

x = 5 * (90° - x)

x = 450° - 5x

x + 5x = 450°

6x = 450°

x = 450°/6

x = 75°

The measure of the other angle is

y = 90° - 75°

y = 15°

The angles are 75° and 15°.

I hope it helps. =)

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3 years ago

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2 years ago

A boat is being pulled into a dock with a rope attached to the boat at water level. When the boat is 12 feet from the dock, the

Natali5045456 [20]

Given :

A boat is being pulled into a dock with a rope attached to the boat at water level. When the boat is 12 feet from the dock, the length of the rope form the boat to the dock is 3 feet longer than twice the height of the dock above the water.

To Find :

The height of the dock.

Solution :

This will make a right angle triangle as given in link below .

Now , applying Pythagoras theorem :

$(2h+3)^2=h^2+12^2\\\\4h^2+9h+9=h^2+144\\\\h^2+4h-45=0\\\\(h-5)(h+9)=0$

Now , h = 5 or h = -9 .

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Hence , this is the required solution .

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