Question
Find x.
- 12
Hint:
We are given a right-angled triangle. We are given one of its side. It is a 30°-60°-90° triangle. We are asked to find the value of its other side. It is denoted by the variable “x”.
The correct answer is:
Let the given triangle be ABC.
∠ABC = 90°
∠BCA = 60°
∠BAC = 30°
BC = x
AB = 1
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= 6
Length of longest side = x
So we can write,
Length of longer side = √3(length of smaller side)
AB = √3(BC)
6 = √3(x)
We will divide the both sides by √3 and rearranging the equation for x.
x = 6 ÷ √3
x = (3 × 2) ÷ √3
x = 2√3
Therefore, the length of x is 2√3.
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.
Related Questions to study
The measure of side b is _____________
For such questions, we should know properties of the right-angled triangle and isosceles triangle.
The measure of side b is _____________
For such questions, we should know properties of the right-angled triangle and isosceles triangle.
A square has side length 95. Calculate the length of the diagonal of the square. Express your answer in simplest radical form.
For such questions, we should know properties of square and right-angled triangle.
A square has side length 95. Calculate the length of the diagonal of the square. Express your answer in simplest radical form.
For such questions, we should know properties of square and right-angled triangle.
Find 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 and using trigonometric ratios.
Find 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 and using trigonometric ratios.
Find the value of x.
For such questions, we should know the properties of right-angled triangle.
Find the value of x.
For such questions, we should know the properties of right-angled triangle.
Find the value of x.
For such questions, we should the properties of both right-angled triangle and isosceles triangle.
Find the value of x.
For such questions, we should the properties of both right-angled triangle and isosceles triangle.
Find x - the length of the hypotenuse of the triangle.
For such questions, we should know properties of different triangles. triangles.
Find x - the length of the hypotenuse of the triangle.
For such questions, we should know properties of different triangles. triangles.
Find the values of a and b.
If your answers are not integers, it should be in
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.
Find the values of a and b.
If your answers are not integers, it should be in
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.
_____ side is the long leg in this 30-60-90 triangle.
For such questions, we should know the properties of a 30°-60°-90° triangle.
_____ side is the long leg in this 30-60-90 triangle.
For such questions, we should know the properties of a 30°-60°-90° triangle.
Find the length of y in this 45-45-90 triangle.
For such questions, we should know different properties of triangles.
Find the length of y in this 45-45-90 triangle.
For such questions, we should know different properties of triangles.
A ramp on a moving truck makes a 30° angle with the ground. The length of the ramp if it is? 5 ft tall? Round to the 10ths place (one decimal place) if necessary.
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.
A ramp on a moving truck makes a 30° angle with the ground. The length of the ramp if it is? 5 ft tall? Round to the 10ths place (one decimal place) if necessary.
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.
Calculate the length of x in this 45-45-90 triangle.
For such questions, we should know the properties of 45°-45°-90° theorem.
Calculate the length of x in this 45-45-90 triangle.
For such questions, we should know the properties of 45°-45°-90° theorem.
The Pythagorean Theorem ONLY works on ______ triangle
The Pythagorean Theorem ONLY works on ______ triangle
Use the 45-45-90 theorem to solve for the hypotenuse.
For such questions, we should the properties of 45°-45°-90° triangle.
Use the 45-45-90 theorem to solve for the hypotenuse.
For such questions, we should the properties of 45°-45°-90° triangle.
What is the length of y in this picture?
For such questions, we should know the properties of different triangles.
What is the length of y in this picture?
For such questions, we should know the properties of different triangles.
Find u 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 and using trigonometric ratios.
Find u 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 and using trigonometric ratios.
