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

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Example Questions

Example Question #11 : Acute / Obtuse Triangles

If the area of an isosceles triangle is $\displaystyle 50$ and its base is $\displaystyle 10$, what is the height of the triangle?

Possible Answers:

$\displaystyle 15$

$\displaystyle 20$

$\displaystyle 10$

$\displaystyle 5$

Correct answer:

$\displaystyle 10$

Explanation:

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

$A=\frac{1}{2}(b)(h)$ $\displaystyle A=\frac{1}{2}(b)(h)$

$50=\frac{1}{2}(10)(h)$ $\displaystyle 50=\frac{1}{2}(10)(h)$

h=10 $\displaystyle h=10$

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Example Question #181 : Geometry

Find the height of the isosceles triangle above if the length of $\overline{AB}=12$ $\displaystyle \overline{AB}=12$ and $\overline{BC}=8$ $\displaystyle \overline{BC}=8$. If your answer is in a decimal form, round to the nearest tenths place.

Possible Answers:

9.8 $\displaystyle 9.8$

11.8 $\displaystyle 11.8$

10.3 $\displaystyle 10.3$

10.8 $\displaystyle 10.8$

11.3 $\displaystyle 11.3$

Correct answer:

11.3 $\displaystyle 11.3$

Explanation:

Because this is an isosceles triangle, $\overline{AC}=\overline{AB}$ $\displaystyle \overline{AC}=\overline{AB}$. Also, we know that the base of the triangle, $\overline{BC}=8$ $\displaystyle \overline{BC}=8$. 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:

$12^{2} = 4^2+h^2$ $\displaystyle 12^{2} = 4^2+h^2$

$h = \sqrt{12^2-4^2}$ $\displaystyle h = \sqrt{12^2-4^2}$

h=11.3 $\displaystyle h=11.3$

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Example Question #11 : Acute / Obtuse Triangles

The triangle above has an area of $\displaystyle 15$ units squared. If the length of the base is $\displaystyle 10$ units, what is the height of the triangle?

Possible Answers:

1.5 $\displaystyle 1.5$

$\displaystyle 5$

$\displaystyle 6$

$\displaystyle 3$

4.5 $\displaystyle 4.5$

Correct answer:

$\displaystyle 3$

Explanation:

The area of a triangle is found using the formula

$A=\frac{1}{2}(base)(height)$ $\displaystyle A=\frac{1}{2}(base)(height)$

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:

$h = \frac{2A}{b} = \frac{2(15)}{10} = 3$ $\displaystyle h = \frac{2A}{b} = \frac{2(15)}{10} = 3$

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

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #11 : Acute / Obtuse Triangles

Example Question #181 : Geometry

Example Question #11 : Acute / Obtuse Triangles

All ACT Math Resources

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