Best Answer

Using trigonometry: height = 15.58845727 units and base = 9 units

Area = 1/2*15.58845727*9 = 70.148 square units to 3 d.p.

Q: What is the area of a 30-60-90 triangle if the hypotenuse is 18?

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hypotenuse = 18/cos60 = 36

and the question is?

Not enough information has been given to solve this problem.

12.728 (rounded)

It can have any area greater than 0 cm2 and less than or equal to 81(3-√8) ≈ 13.897 cm2. Without further information that provides the length of (at least) one side it is impossible to say which of these areas the triangle has. For example: base = 9 cm, hypotenuse = 9 cm ⇒ height = 18 - 9 - 9 cm = 0 cm ⇒ area = 9x0/2 = 0 cm2 This triangle does not actually exist and represents the minimum of the area. base = 6 cm, hypotenuse = 7.5 cm ⇒ height = 18 - 6 - 7.5 cm = 4.5 cm ⇒ area = 6x4.5/2 = 12.5 cm2 Note that base2 + height2 = 36 + 20.25 = 56.25 = 7.52 = hypotenuse2 and so this is a right angle triangle. base = 9(2-√2) cm ≈ 5.272 cm, hypotenuse = 18(√2 -1) cm ≈ 7.456 cm ⇒ height = 18 - 9(2-√2) - 18(√2 -1) cm = 9(2-√2) cm ≈ 5.272 cm ⇒ area = 9(2-√2) x 9(2-√2)/2 = 81(3-√8) cm2 ≈ 13.897 cm2 This triangle is a right angle triangle (check out Pythagoras on the lengths) and is the right angle triangle of largest area with perimeter 18 cm.

Related questions

The hypotenuse of a triangle 18" x 18" is: 25.46 inches

hypotenuse = 18/cos60 = 36

and the question is?

Not enough information has been given to solve this problem.

If a 45- 45- 90 triangle has a hypotenuse of length 18 units, the length of both of the other legs is: 12.73 units.

If the 7" and 18" are the two legs, then the hypotenuse is 19.313" (rounded). If the 18" is the hypotenuse, then the missing leg is 16.583" (rounded).

Use Pythagoras' theorem: 182+122 = 468 and the square root of this is the hypotenuse which is about 21.63330765 units in length

Using trigonometry and Pythagoras' theorem the length of the hypotenuse is 36

Using Pythagoras' theorem for a right angle triangle its hypotenuse is 82 units in length

It can have any area greater than 0 cm2 and less than or equal to 81(3-√8) ≈ 13.897 cm2. Without further information that provides the length of (at least) one side it is impossible to say which of these areas the triangle has. For example: base = 9 cm, hypotenuse = 9 cm ⇒ height = 18 - 9 - 9 cm = 0 cm ⇒ area = 9x0/2 = 0 cm2 This triangle does not actually exist and represents the minimum of the area. base = 6 cm, hypotenuse = 7.5 cm ⇒ height = 18 - 6 - 7.5 cm = 4.5 cm ⇒ area = 6x4.5/2 = 12.5 cm2 Note that base2 + height2 = 36 + 20.25 = 56.25 = 7.52 = hypotenuse2 and so this is a right angle triangle. base = 9(2-√2) cm ≈ 5.272 cm, hypotenuse = 18(√2 -1) cm ≈ 7.456 cm ⇒ height = 18 - 9(2-√2) - 18(√2 -1) cm = 9(2-√2) cm ≈ 5.272 cm ⇒ area = 9(2-√2) x 9(2-√2)/2 = 81(3-√8) cm2 ≈ 13.897 cm2 This triangle is a right angle triangle (check out Pythagoras on the lengths) and is the right angle triangle of largest area with perimeter 18 cm.

12.728 (rounded)

H = sqrt (324 + 576) = sqrt 900 = 30 in