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

Study concepts, example questions & explanations for ACT Math

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Example Questions

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

A triangle has a perimeter of 36 inches, and one side that is 12 inches long. The lengths of the other two sides have a ratio of 3:5. What is the length of the longest side of the triangle?

Possible Answers:

14

9

12

8

15

Correct answer:

15

Explanation:

We know that the perimeter is 36 inches, and one side is 12. This means, the sum of the lengths of the other two sides are 24. The ratio between the two sides is 3:5, giving a total of 8 parts. We divide the remaining length, 24 inches, by 8 giving us 3. This means each part is 3. We multiply this by the ratio and get 9:15, meaning the longest side is 15 inches.

Example Question #2 : How To Find The Length Of The Side Of An Acute / Obtuse Triangle

_tri61

What is the value of  in the triangle above? Round to the nearest hundredth.

Possible Answers:

Cannot be computed

Correct answer:

Explanation:

What is the value of  in the triangle above? Round to the nearest hundredth.

Begin by filling in the missing angle for your triangle. Since a triangle has a total of  degrees, you know that the missing angle is:

Draw out the figure:

_tri62

Now, to solve this, you will need some trigonometry. Use the Law of Sines to calculate the value:

Solving for , you get:

Rounding, this is .

Example Question #3 : How To Find The Length Of The Side Of An Acute / Obtuse Triangle


_tri21

What is the value of  in the triangle above? Round to the nearest hundredth.

Possible Answers:

Cannot be computed

Correct answer:

Explanation:

Begin by filling in the missing angle for your triangle. Since a triangle has a total of  degrees, you know that the missing angle is:

Draw out the figure:

_tri22

Now, to solve this, you will need some trigonometry. Use the Law of Sines to calculate the value:

Solving for , you get:

Rounding, this is .

Example Question #4 : How To Find The Length Of The Side Of An Acute / Obtuse Triangle

_tri31

What is the length of side ? Round to the nearest hundredth.

Possible Answers:

Cannot be computed

Correct answer:

Explanation:

Begin by filling in the missing angle for your triangle. Since a triangle has a total of  degrees, you know that the missing angle is:

Draw out the figure:

_tri32

This problem becomes incredibly easy! This is an isosceles triangle. Therefore, you know that  is , because it is "across" from a  degree angle—which matches the other  degree angle!

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