There are two types of special right triangles
In a 45-45-90 triangle
the hypotenuse is 2 times as long as a leg
An isosceles right triangle is also called a 45-45-90 triangle.
In a 30 - 60 - 90 triangle,
the hypotenuse = twice as long as the shorter leg
and
the longer leg = √3 times as long as the shorter leg.
Find the value of x in each triangle
Problem 1 :
Solution :
It comes under 45-45-90 right triangle.
Hypotenuse (y) = 2(Smallest sides)
y = 2(5)
y = 10
x = 5
Problem 2 :
Solution :
It comes under 30-60-90 right triangle.
Hypotenuse = b
Smallest leg = 12
Longer leg (a) = √3(shorter leg)
= 12√3
Hypotenuse = 2(shorter leg)
= 2(12)
= 24
Problem 3 :
Solution :
Hypotenuse = 8
Shorter leg = c
c = d
Hypotenuse = 2(Shorter leg)
8 = 2c
c = 4 and d = 4
Problem 4 :
Solution :
Shorter leg = c, hypotenuse = 10, longer leg = d
2(Shorter leg) = 10 2c = 10 c = 5 |
Longer leg = √3(5) d = 5√3 |
Problem 5 :
Solution :
Shorter leg = r = 16, hypotenuse = q
Hypotenuse = 2(Shorter leg)
q = 2(16)
q = 32
Problem 6 :
Solution :
Hypotenuse = m
Shorter leg = 6 and
longer leg = p
Hypotenuse = 2(Shorter leg)
m = 2(6)
m = 12
Longer leg = √3 (shorter leg)
P = 6√3
Problem 7 :
Solution :
Hypotenuse = h
Shorter leg = f and
longer leg = 8
Longer leg = √3 (shorter leg)
8 = √3(f)
f = 8/√3
f = (8/√3) ⋅ (√3/√3)
f = 8√3/3
Hypotenuse (h) = 2(shorter leg)
= 2(8√3/3)
= 16√3/3
Problem 8 :
Solution :
Hypotenuse = 6√2
Shorter leg = n
Hypotenuse = 2(Shorter leg)
6√2 = 2n
n = 3√2
Problem 9 :
The side length of an equilateral triangle is 5 cm. Find the length of an altitude of the triangle.
Solution :
Shorter leg = CD = 2.5
Longer leg = AC
Hypotenuse = AD = 5
Longer leg = √3(Shorter leg)
= √3(2.5)
= 2.5√3
Problem 10 :
The perimeter of the square is 36 inches. Find the length of the diagonal.
Solution :
Let x be the side length of square.
Perimeter of the square = 36
4x = 36
x = 9
Using Pythagorean theorem :
x^{2} + x^{2} = (Length of diagonal)^{2}
9^{2} + 9^{2} = (Length of diagonal)^{2}
81 + 81 = (Length of diagonal)^{2}
Length of diagonal = √162
= 9√2
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM