In the figure AC = 5 cm. , What is the length of AB ?.( Correct to two decimal
places)
Answers
Answer:
Plz attach the appropriate figure.
Step-by-step explanation:
We are given that In right ∆ABC, the length of AC is 5cm, the angle of B is 90° and the angle of C is 45°. With this information, we are asked to calculate the length of AB. i.e.
AC = 5cm
∠B = 90°
∠C = 45°
AB = ?
So, we need toSo, we need to calculate the length of AC.
We know that, The sum of all internal angles of a triangle is always equal to 180 degrees.
In right ∆ABC, we have;
\implies \rm{\angle A + \angle B + \angle C = 180^\circ}⟹∠A+∠B+∠C=180
∘
\implies \rm{\angle A + 90^\circ + 45^\circ = 180^\circ}⟹∠A+90
∘
+45
∘
=180
∘
\implies \rm{\angle A + 135^\circ = 180^\circ}⟹∠A+135
∘
=180
∘
\implies \rm{\angle A = 180^\circ - 135^\circ}⟹∠A=180
∘
−135
∘
\implies \rm{\angle A = 45^\circ}⟹∠A=45
∘
So from here we can conclude that it is a isosceles right angle triangle. Therefore, AB = BC, since it is a isosceles right angle triangle.
By using Pythagoras theorem in right ∆ABC, we have;
\implies \rm{AC^2 = AB^2+BC^2}⟹AC
2
=AB
2
+BC
2
\implies \rm{AC = AB^2 + AB^2}⟹AC=AB
2
+AB
2
\implies \rm{AC = 2AB^2}⟹AC=2AB
2
\implies \rm{5 = 2AB^2}⟹5=2AB
2
\implies \rm{AB^2 = \dfrac{5}{2}}⟹AB
2
=
2
5
\implies \rm{AB^2 = 2.5}⟹AB
2
=2.5
\implies \rm{AB = \sqrt{2.5}}⟹AB=
2.5
\implies \boxed{\bf{AB = 1.58}}⟹
AB=1.58
Hence, the length of AB is 1.58cm approximately.
\rule{90mm}{2pt}