The angle created in a semicircle is 90°. Then, we will be having a right triangle. Using Pythagorean theorem, we can find the missing side of a right triangle.
Calculate
the length of sides labelled in the circles below
Problem 1 :
Solution :
Here ∠BAC = 90
Using Pythagorean theorem :
AB^{2} + AC^{2} = BC^{2}
8^{2} + x^{2} = 10^{2}
64 + x^{2} = 100
x^{2} = 100 – 64
x^{2} = 36
x = 6
So, the value of x is 6 cm.
Problem 2 :
Solution :
∠BAC = 90
Using Pythagorean theorem :
AB^{2} + AC^{2} = BC^{2}
5^{2} + 12^{2} = x^{2}
25 + 144 = x^{2}
x^{2} = 144 + 25
x^{2} = 169
x = 13
So, the value of x is 13 cm.
Problem 3 :
Solution :
AC^{2} + BC^{2} = AB^{2}
6^{2} + 6^{2} = x^{2}
36 + 36 = x^{2}
72 = x^{2}
x = 8.48
So, the value of x is 8.48 cm.
Calculate
the length of sides labelled in the circles below
Problem 4 :
Solution :
In the right triangle ABC,
AB = Opposite side, AC = Adjacent side and BC = Hypotenuse
cos θ = Adjacent side / Hypotenuse
cos 28 = AC/BC
cos 28^{º }= x/12
0.882 = x/12
x = 0.882(12)
x = 10.58
So, the value of x is 10.58.
Problem 5 :
Solution :
In the right triangle ABC,
AB = Hypotenuse, AC = Opposite side and BC = Adjacent side.
sin 55^{º} = opposite/hypotenuse
= AC/AB
= x/9
0.82 = x/9
x = 0.82 × 9
x = 7.38
So, the value x is 7.38.
Problem 6 :
Solution :
In the right triangle ABC, AB = Hypotenuse, BC = Opposite side and AC = Adjacent side
tan 49^{º} = opposite/adjacent
tan 49 = BC/AC
1.15 = 8/AC
AC = 8/1.15
AC = 6.95
AC = 7 cm
So, the value of x is 7 cm.
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