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30 60 90 Triangles:

 

The 30-60-90 triangle is a special right triangle, as it has a special relationship between its sides. If we know the measure of at least one side of the triangle, the special proportions of sides of the 30-60-90 triangle could be used to determine the measure of other sides of the same triangle. 


These special relations between the sides of the 30-60-90 triangle are the result of the Pythagorean theorem.


Triangle 1

 

30 60 90 Triangles Sample Questions:

Question 1: In the following 30-60-90 triangle, determine the measure of the hypotenuse.


Triangle 2


Answer: 4 Unit

Explanation: The given measure is the shorter leg of the 30-60-90 triangle. And, we know the hypotenuse of the 30-60-90 triangle, is twice the measure of the shorter leg.

 

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Question 2: In the following 30-60-90 triangle, determine the measure of the longer side.

 

Triangle 3

Answer: 3√3 Unit

Explanation: The given measure is the shorter leg of the 30-60-90 triangle. And, we know the longer side of the 30-60-90 triangle, is square root three times the measure of the shorter leg.

 

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Question 3: Determine the measure of the shorter side.

 

Triangle 4
Answer: 3√3 Unit

Explanation: The given measure is the longer leg of the 30-60-90 triangle. And, we know the longer side of the 30-60-90 triangle, is square root three times the measure of the shorter leg.

 

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Question 4: Determine the measure of the hypotenuse.

 

Triangle 5


Answer: 8 Unit

Explanation: The given measure is the shorter leg of the triangle. And, we know the hypotenuse of the 30-60-90 triangle, is twice the measure of the shorter leg.

 

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Question 5: Does the length of sides 2 cm, 23 cm, and 4 cm, represent a 30-60-90 triangle?


Answer: Yes

Explanation: The given measure of the sides are: 2 cm, 2√3 cm, and 4 cm.

Now, let us divide the proportion by 2. We get, 1 cm, √3 cm, and 2 cm.

 

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Question 6: Does the length of sides 3 cm, 63 cm, and 9 cm, represent a 30-60-90 triangle?


Answer: No

Explanation: The given measure of the sides are: 3 cm, 6√3 cm, and 9 cm.

Now, let us divide the proportion by 3. We get, 1 cm, 2√3 cm, and 2 cm.

 

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Question 7: For the following 30-60-90 triangle, determine the measure of the unknown side.

 

Triangle 6


Answer: x=5 unit, y=5√3 unit.

Explanation: We have given the measure of the hypotenuse. And, we know the hypotenuse of the 30-60-90 triangle, is twice the measure of the shorter leg. 

 

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Question 8: Determine the measure of the unknown side.

 

Triangle 7


Answer: a=4 unit, b=8 unit.

Explanation: We have given the measure of the longer side. And, we know the longer side of the 30-60-90 triangle is square root three times the measure of the shorter leg.

 

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Question 9: The length of the hypotenuse of the 30-60-90 triangle is 12 cm. What would be the measure of the other two sides?


Answer: 6 cm, 6√3 cm

Explanation: We have given the measure of the hypotenuse. And, we know the hypotenuse of the 30-60-90 triangle, is twice the measure of the shorter leg.

 

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Question 10: The length of the longer side of the 30-60-90 triangle is 73 cm. What would be the measure of the other two sides?


Answer: 7 cm, 14 cm

Explanation: We have given the measure of the longer side. And, we know the longer side of the 30-60-90 triangle is square root three times the measure of the shorter leg.

 

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Frequently Asked Questions:

Question 1: How to solve 30 60 90 triangles?

 

30-60-90 is a special type of right triangle in which angles are in the ratio of 1:2:3 and sides are in ratio 1:√3:2.


We can solve according to the given values of the corresponding sides.
 

Triangle 8

 

Question 2: How to find the sides of a 30 60 90 triangle?

In 30-60-90 triangles we use the triangle rule to find the sides.

 

  • When base BC base is given, by triangle rule we   calculate all the rest sides.
     

Triangle 9

 

  • When perpendicular AB is given,by triangle rule we calculate all the rest sides.
     

Triangle 10

 

  • When hypotenuse AC is given,by triangle rule we calculate the remaining sides
     

Triangle 11

 

Question 3: Which triangle is a 30°-60°-90° triangle?

A right triangle having angles of  30°,  60°, and 90° is known as a 30-60-90 triangle The sides are always in the same ratio to each other since the angles are always in that ratio.

 

Question 4: How to find the area of a 30 60 90 triangle?

The total space occupied by the three sides of a triangle is called its area. The basic formula is half of the product of its base and height. The 30-60-90 triangle is a right-angled triangle and its sides are always in the same ratio 1: √3:2.

 

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