# GMAT Math : Calculating the height of an acute / obtuse triangle

## Example Questions

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### Example Question #62 : Acute / Obtuse Triangles

Given:  with  and .

Construct the altitude of  from  to a point  on . What is the length of ?

Explanation:

is shown below, along with altitude .

Since , and , by definition, is perpendicular to  is a 30-60-90 triangle. By the 30-60-90 Triangle Theorem, , as the shorter leg of , has half the length of hypotenuse ; this is half of 30, or 15.

### Example Question #63 : Acute / Obtuse Triangles

Given:  with , construct two  altitudes of : one from  to a point  on , and another from  to a point  on . Which of the following is true of the relationship of the lengths of  and ?

The length of  is four-ninths that of

The length of  is twice that of

The length of  is nine-sixteenths that of

The length of  is two-thirds that of

The length of  is three-fourths that of

The length of  is three-fourths that of

Explanation:

The area of a triangle is one half the product of the length of any base and its corresponding height; this is , but it is also . Set these equal, and note the following:

That is, the length of  is three fourths that of that of

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