ACT Math : How to find the height of an acute / obtuse triangle

Example Questions

Example Question #1 : How To Find The Height Of An Acute / Obtuse Triangle

If the area of an isosceles triangle is  and its base is , what is the height of the triangle?

Explanation:

Use the formula for area of a triangle to solve for the height:

Example Question #182 : Act Math

Find the height of the isosceles triangle above if the length of  and . If your answer is in a decimal form, round to the nearest tenths place.

Explanation:

Because this is an isosceles triangle, . Also, we know that the base of the triangle, . Therefore, we create two triangles by bisecting the trinagle down the center. We are solving for the length of the long arm of the triangle. We know that the hypotenuse is 12 and the base is 4 (half of 8).

Thus we use the Pythagorean Theorem to find the length of the long arm:

Example Question #183 : Act Math

The triangle above has an area of  units squared. If the length of the base is  units, what is the height of the triangle?

Explanation:

The area of a triangle is found using the formula

The height of any triangle is the length from it's highest point to the base, as pictured below:

We can find the height by rearranging the area formula: