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.
30 60 90 Triangles Sample Questions:
Question 1: In the following 30-60-90 triangle, determine the measure of the hypotenuse.
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.
Question 2: In the following 30-60-90 triangle, determine the measure of the longer side.
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.
Question 3: Determine the measure of the shorter side.
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.
Question 4: Determine the measure of the hypotenuse.
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.
Question 5: Does the length of sides 2 cm, 2√3 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.
Question 6: Does the length of sides 3 cm, 6√3 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.
Question 7: For the following 30-60-90 triangle, determine the measure of the unknown side.
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.
Question 8: Determine the measure of the unknown side.
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.
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.
Question 10: The length of the longer side of the 30-60-90 triangle is 7√3 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.
Take 30-60-90 Triangles Homework Help Today!
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.
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.
- When perpendicular AB is given,by triangle rule we calculate all the rest sides.
- When hypotenuse AC is given,by triangle rule we calculate the remaining sides
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.