How to find the length of the side of an acute / obtuse triangle - ACT Math
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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?
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?
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.
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.
Compare your answer with the correct one above
What is the value of 
in the triangle above? Round to the nearest hundredth.
What is the value of
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:
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 
.
What is the value of
Begin by filling in the missing angle for your triangle. Since a triangle has a total of
Draw out the figure:
Now, to solve this, you will need some trigonometry. Use the Law of Sines to calculate the value:
Solving for
Rounding, this is
Compare your answer with the correct one above
What is the value of 
in the triangle above? Round to the nearest hundredth.
What is the value of
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:
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 
.
Begin by filling in the missing angle for your triangle. Since a triangle has a total of
Draw out the figure:
Now, to solve this, you will need some trigonometry. Use the Law of Sines to calculate the value:
Solving for
Rounding, this is
Compare your answer with the correct one above
What is the length of side 
? Round to the nearest hundredth.
What is the length of side
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:
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!
Begin by filling in the missing angle for your triangle. Since a triangle has a total of
Draw out the figure:
This problem becomes incredibly easy! This is an isosceles triangle. Therefore, you know that
Compare your answer with the correct one above