General
General
Easy
Question
Find a in this 30-60-90 triangle.
- a = 14
Hint:
We are given a right-angled triangle. We are given one of its angle. It is 60°. Then, the other angle will be 30°. We are given the values of its one of its side. It is 7√3. We are asked to find it’s hypotenuse.
The correct answer is: a = 14
Let the given triangle be ABC.
∠ABC = 90°
∠BAC = 30°
AB = b
BC = 7√3
AC = a
The sum of all angles of a triangle is 180°. Therefore, the remaining angle will be 30°
So, ∠BCA = 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 AB.
Length of smallest side = b
Hypotenuse = a
The length of longer side is 7√3
So we can write,
Length of longer leg = √3 ( length of smaller leg)
BC = √3(AB)
So, to find the smaller leg we have to divide the longer side by √3.
AB = BC ÷ √3
AB = 7√3 ÷ √3
b = 7
Now,
Hypotenuse = 2(length of smallest side)
AC = 2(7)
a = 14
Therefore, the length of the hypotenuse is 14.
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 trigonometric ratios.
Related Questions to study
General
Find the value of x.
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.
Find the value of x.
GeneralGeneral
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.
General
Find the length of u and v in this 30-60-90 triangle.
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.
Find the length of u and v in this 30-60-90 triangle.
GeneralGeneral
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.
maths-
Three coins of unit radius are placed in an equilateral triangle as shown in the following figure The area of the equilateral triangle is
Three coins of unit radius are placed in an equilateral triangle as shown in the following figure The area of the equilateral triangle is
maths-General
biology
Pith and cortex belongs to -
Pith and cortex belongs to -
biologyGeneral
biology
Which of the following is not the characteristic feature of Cycas :
Which of the following is not the characteristic feature of Cycas :
biologyGeneral
maths-
A random variable x has the following probability distribution:
Determine P(X > 6)
A random variable x has the following probability distribution:
Determine P(X > 6)
maths-General
maths-
If m and 
are the mean and variance of the random variable X, whose distribution is given by:
If m and are the mean and variance of the random variable X, whose distribution is given by:
maths-General
maths-
A random variable X has the following distribution
The value of ‘K’ and P(X<3) are respectively equal to
A random variable X has the following distribution
The value of ‘K’ and P(X<3) are respectively equal to
maths-General
maths-
A random variable X has the following probability distribution
then the mean value of X is
A random variable X has the following probability distribution
then the mean value of X is
maths-General
maths-
If a random variable X has the following probability distribution
then the mean value of X is
If a random variable X has the following probability distribution
then the mean value of X is
maths-General
maths-
If X is a random variable with the following probability distribution
then the variance of X, V(x)=
If X is a random variable with the following probability distribution
then the variance of X, V(x)=
maths-General
maths-
A random variable X has the probability distribution given below. Its variance is
A random variable X has the probability distribution given below. Its variance is
maths-General
maths-
If the probability distribution of a random variable X is
then k =
If the probability distribution of a random variable X is
then k =
maths-General
maths-
If the probability distribution of a random variable X is
then second moment about 0 i.e., 
If the probability distribution of a random variable X is
then second moment about 0 i.e.,
maths-General
maths-
X is a random variable with distribution given below
Then the value of k and variance are
X is a random variable with distribution given below
Then the value of k and variance are
maths-General
