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3 years ago

In a right triangle the leg opposite to the acute angle of 30° is 7 in. Find the hypotenuse and other leg.

Mathematics

2 answers:

fiasKO [112]3 years ago

8 0

Answer:

Hypotenuse = 14in

Adjacent = 12.12in

Step-by-step explanation:

Check attachment for diagram

Using SOH, CAH TOA method

According to SOH

Sin(theta) = Opposite/Hypotenuse

Given theta = 30°

Opposite = 7in

Sin30° = 7/Hypotenuse

Hypotenuse = 7/sin30°

Hypotenuse = 7/0.5

Hypotenuse = 14in

The other leg will be the adjacent say x

Using Pythagoras theorem to get x

Hyp² = Opp²+Adj²

14² = 7²+x²

x² = 14²-7²

x² = 196-49

x² = 147

x = √147

x = 12.12in

The value of the other leg is 12.12

Maksim231197 [3]3 years ago

5 0

This is a 30-60-90 triangle.
Therefore,
7 is A
the other leg is A√3
And the hypotenuse is 2A
So the other leg is 7√3 and the hypotenuse is 14

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3 years ago

How does knowing the double 6+6=12 help you solve the near double 6+7=13

forsale [732]

Answer:

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Step-by-step explanation:

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3 years ago

In parallelogram ABCD , diagonals AC¯¯¯¯¯ and BD¯¯¯¯¯ intersect at point E, BE=2x2−x , and DE=x2+6 .

kondaur [170]

<span>The diagonals of a parallelogram bisect each other. So we just equate the two equations BE and DE 2x^2 - x = x^2 + 6 2x^2 - x - x^2 - 6 = 0 x^2 - x - 6 = 0 This is quadratic eqn. So we obtain. (x - 3) ( x + 2) = 0 Setting each to 0 and solving for x, we have that x = 3 and x = -2 So we have two possible values for BD. But Since BE = DE then we can simply double each If x = 3 BD = 2 (2(3)^2 - 3) = 2 ( 18 - 3) = 30 units If x = - 2 BD = 2((-2)^2 -3 ) = 2 (8 - 3) = 10 units</span>

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Step-by-step explanation:

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Vesna [10]

Answer:

V = 1206.3 $ft^{3}$

Step-by-step explanation:

This shape is made up of a cylinder on the bottom and a cone on the top. We'll find the volumes of these shapes separately and then add them together.

Volume of a cylinder = area (of the base) x height

Substitute in the formula for the area of a circle.

V(cylinder) = $\pi$ $r^{2}$ x h

Substitute in the values for the radius (8) and height (4)

V(cylinder) = $\pi$ x $8^{2}$ x 4

Evaluate using a calculator

V(cylinder) = 804.2477

To the nearest tenth, V(cylinder) = 804.2

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Substitute in the values for the radius of the circle (8) and the height (6)

V(cone) = $\frac{\pi 8^{2} 6 }{3}$ (On the top it's $\pi$ x $8^{2}$ x 6)

Evaluate using a calculator

V(cone) = 402.1239

To the nearest tenth, V(cone) = 402.1

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3 years ago