Question
Find the values of a and b.
If your answers are not integers, it should be in
- a = 4 b = 2
Hint:
We are given a right-angled triangle. We are given the value of its hypotenuse. We are given one of its angle. It is 60°. The other angle will be 30°. We are asked to find the values of the other two sides.
The correct answer is:
Let the given triangle be ABC.
∠ABC = 90°
∠BCA = 60°
AC = 2√2
The sum of all angles of a triangle is 180°.
So, ∠BAC = 30°
It is 30°-60°-90° triangle.
In a 30°-60°-90° triangle, the length of hypotenuse is two times the length of the smallest side. It’s longer side is √3 times the value of the smallest side.
The side opposite to the 30° angle is the smallest side.
The side opposite to the 60° angle is the longer side.
In the given question, the side opposite to 30° is BC. The side opposite to 60° is AB.
Length of smallest side= b
Length of longest side = a
Hypotenuse = 2√2
So we can write,
Hypotenuse = 2(length of the smallest side)
2√2 = 2b
So, to find the smaller leg we have to divide the hypotenuse by 2.
b = 2√2 ÷ 2
b = √2
Therefore, the value of b is √2.
Now,
Length of longer side = √3(length of smaller side)
a = √3(√2)
a = √6
a = √6
Therefore, the length of a is √6.
So, the values are a = √6, b = √2.
For such questions, we should know about the properties of a right-angled triangle and 30°-60°-90° triangle. The alternate way to solve the above question is by Pythagoras theorem and using trigonometric ratios.
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