GMAT Quantitative Reasoning - Calculating the height of an acute / obtuse triangle

Given: $\bigtriangleup ABC$ with $m \angle A = m \angle C = 30 ^{\circ}$ and .

Construct the altitude of $\bigtriangleup ABC$ from to a point on $\overline{AC}$ . What is the length of $\overline{BM}$ ?

Given: $\bigtriangleup ABC$ with $m \angle A = 45^{\circ }$ , $m \angle C = 60 ^{\circ}$ , .

Construct the altitude of $\bigtriangleup ABC$ from to a point on $\overline{AC}$ . What is the length of $\overline{BM}$ ?

Given: $\bigtriangleup ABC$ with

Construct the altitude of $\bigtriangleup ABC$ from to a point on $\overline{BC}$ . Between which two consecutive integers does the length of $\overline{AN}$ fall?

Given: $\bigtriangleup ABC$ with $m \angle A = m \angle C = 30 ^{\circ}$ and .

Construct the altitude of $\bigtriangleup ABC$ from to a point on $\overleftrightarrow{BC}$ . What is the length of $\overline{AN}$ ?

Given: $\bigtriangleup ABC$ with $m \angle A = 45^{\circ }$ , $m \angle C = 30 ^{\circ}$ , .

Construct the altitude of $\bigtriangleup ABC$ from to a point on $\overline{AC}$ . What is the length of $\overline{BM}$ ?

Given: $\bigtriangleup ABC$ with $m \angle A = m \angle C = 30 ^{\circ}$ .

Construct two altitudes of $\bigtriangleup ABC$ : one from to a point on $\overline{AC}$ , and the other from to a point on $\overleftrightarrow{BC}$ . Give the ratio of the length of $\overline{AN}$ to that of $\overline{BM}$ .

Given: $\bigtriangleup ABC$ with $m \angle A = m \angle C = 30 ^{\circ}$ and .

Construct the altitude of $\bigtriangleup ABC$ from to a point on $\overline{AC}$ . What is the length of $\overline{BM}$ ?

Given: $\bigtriangleup ABC$ with , construct three altitudes of $\bigtriangleup ABC$ - one from to a point on $\overleftrightarrow{BC}$ , another from to a point on $\overleftrightarrow{AC}$ , and a third from to a point on $\overleftrightarrow{AB}$ . Order the altitudes, $\overline{AM}$ , $\overline{BN}$ , and $\overline{CO}$ from shortest to longest.

Given: $\bigtriangleup ABC$ with , construct two altitudes of $\bigtriangleup ABC$ : one from to a point on $\overleftrightarrow{BC}$ , and another from to a point on $\overleftrightarrow{AC}$ . Which of the following is true of the relationship of the lengths of $\overline{AM}$ and $\overline{BN}$ ?

The largest angle of an obtuse isosceles triangle is $120^{\circ}$ . If two of the sides have an equal length of , what is the height of the triangle?

Calculating the height of an acute / obtuse triangle

Practice Questions