Mathematics

Grade9

Easy

Question

Find the value of y.

8
4
2√3
8√3

hint Hint:

We are given a right-angled triangle. From the figure, we can observe that the value of one side is 4√3 . We are given the value of other two angles. They are 30° and 60°. We are asked to find the value of hypotenuse. Hypotenuse is the longest side. It is opposite to the angle of 90°. For a right-angled triangle, we can use the relation between the angles and the sides to find the required value.

The correct answer is: 8

The value of one of the side is 4√3. This side is opposite to the angle 60 degree.
The other angles of the triangle are 30° and 60°.
The value of hypotenuse is represented using a variable “y”.
We will use the properties of right-angled triangle.
If “A” is a angle of right – angled triangle, then we can write
$S i n A equals space fraction numerator O p p o s i t e space s i d e space over denominator H y p o t e n u s e end fraction$
As side opposite to 60° is given, we will use that angle to find the required value.
We will substitute the values in the above equation.
A = 60°
Opposite side = 4√3
Hypotenuse = y
$S i n 60 space equals space fraction numerator 4 square root of 3 over denominator y end fraction T h e space v a l u e space o f space S i n 60 space i s space fraction numerator square root of 3 over denominator 2 end fraction W e space w i l l space r e a r r a n g e space t h e space e q u a t i o n space f o r space y. y space equals space fraction numerator 4 square root of 3 over denominator begin display style fraction numerator square root of 3 over denominator 2 end fraction end style end fraction y space equals space 4 square root of 3 space space cross times space fraction numerator 2 over denominator square root of 3 end fraction space space space space equals space 8$
y = 8
Therefore, the value of the hypotenuse is 8.

For such questions, we should know the properties of right-angled triangle. We should know the trignometric ratios. The values of different sines and cosines should be known.

A square has side length 95. The length of the diagonal of the square is? Express your answer in simplest radical form.

For such questions, we should know the properties of the right-angled triangle. The other method to solve it will be 45°-45°-90° theorem. Due to diagonal, the triangle which is formed has the sides in proportion 1:1:√2. Therefore, the value of hypotenuse is given by √2 multiplied by the value of the side.

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Find the value of y.

842√38√3

The correct answer is: 8

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8
4
2√3
8√3