30-60-90 Triangles
30-60-90 trianglesAnother type of special right triangles is the 30°- 60°- 90° triangle. This is right triangle whose angles are 30°, 60°and 90°. The lengths of the sides of a 30°- 60°- 90° triangle are in the ratio 1:√3:2
Side1: Side2 : Hypotenuse = a : a√3 : 2a

Some Solved Examples
Example 1 : Find the length of the hypotenuse, if the two sides are 5√3 and 5.
Solution :
As the two sides fit in the ratio a : a√3 : 2a
a = 5
Hypotenuse = 2a
Hypotenuse = 2 x 5 = 10
Example 2 : Find x and y

Solution :
As the given triangle is a special triangle of 30 - 60 -90.
The ratio for this triangle is Side1: Side2 : Hypotenuse = a : a√3 : 2a
Here hypotenuse = 2a = 16
So, a = 8
y = 8
x = 8√3
___________________________________________________________________
2) In a right triangle, the longest side is 12cm. Find the long leg and short leg.
Solution :
Longest side= Hypotenuse (H)= 12 cm (side opposite to 90 0
Short leg is the side across 30 0
SL = ½ x H
SL = ½ x 12 = 6cm
Long leg is the side across 60 0
LL = SL x √3
LL = 6√3 cm
__________________________________________________________________
3)In Δ ABC, AC= 14 cm; BC= 7 cm and AB= 7√3 cm. Find the measures of angles A, B and C.
Solution
AC = 14cm; BC = 7cm and AB =7√3cm
From the above information we can see that, AC = 2 x BC and it is longest side than the other two.
So, AC will be the hypotenuse.
The angle between AC is B
So,∠B = 90 0
BC = 7cm which is the one half of hypotenuse.
So, short leg = SL = 7cm
∴ ∠A = 30 0
AB= 7√3cm which is √3 times SL
∴ ∠C = 60 0
Special Right Triangles
Special Right Triangles
30-60-90 Triangles
Pythagorean Theorem
GMAT
GRE
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th Grade
7th grade math
8th grade math
9th grade math
10th grade math
11th grade math
Precalculus
Worksheets
Chapter wise Test
MCQ's
Math Dictionary
Graph Dictionary
Multiplicative tables
Math Teasers
NTSE
Chinese Numbers
CBSE Sample Papers