How to find the height of an acute / obtuse triangle - Intermediate Geometry

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Question

Find the height of the triangle shown above.

Answer

Use the Pythagorean Theorem to find the height of this triangle: , where the height of the triangle.

$a=\sqrt{64}=8$

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Question

Find the height of the obtuse triangle shown above.

Answer

To solve this solution, first work backwards using the formula:

$Area=\frac{b\cdot h}{2}$

Plugging in the given values we are able to solve for the height.
$27=\frac{9h}{2}$

$h=\frac{54}{9}=6$

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Question

Find the height of the acute triangle shown above.

Answer

To solve this solution, work backwards using the formula:

$Area=\frac{b\cdot h}{2}$

Plugging in the given values we are able to solve for the height.
$160=\frac{16h}{2}$

$h=320\div16=20$

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Question

A triangle has a base of and an area of square units. Find the height of the triangle.

Answer

To solve this solution, work backwards using the formula:

$Area=\frac{b\cdot h}{2}$

Plugging in the given values we are able to solve for the height.
$9=\frac{3h}{2}$

$h=18\div3=6$

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Question

An obtuse triangle has a base of and an area of square units. Find the height of the triangle.

Answer

To solve this solution, work backwards using the formula:

$Area=\frac{b\cdot h}{2}$

Plugging in the given values we are able to solve for the height.

$225=\frac{30h}{2}$

$h=\frac{450}{30}=15$

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Question

An obtuse triangle has a base of and an area of square units. Find the height of the triangle.

Answer

To solve this solution, first work backwards using the formula:

$Area=\frac{b\cdot h}{2}$

Plugging in the given values we are able to solve for the height.
$450=\frac{45h}{2}$

$h=900\div45=20$

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