Question
A triangle has side lengths: 8, 8√3, 16. Is this triangle a right triangle, an acute triangle, or an obtuse triangle?
- Right
- Acute
- Obtuse
- Equilateral
Hint:
We are given the sides of a right-angled triangle. It is 8, 8√3 and 16. We are asked if the triangle is an acute or an obtuse triangle. An obtuse triangle means one of the angle of the triangle is greater than 90°. An acute angle means all of the angles of the triangle are less than 90°. One of the angle will be 90° for right-angled triangle.
The correct answer is: Right
The values of given sides are 8, 8√3 and 16.
We will take the ratios of the sides.
The ratio is 1:√3:2.
This ratio is seen in a triangle 30°-60°-90°.
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.
So, the angles of the triangles are 30°,60° and 90°. If we see, all the angles are less than 90° or equal to 90°.
It means the triangle is an acute triangle.
The given triangle is an acute triangle.
Related Questions to study
Find the value of a and b. Leave your answers in simplest radical form.
For such questions, we should know the properties of right-angled triangle and isosceles triangle.
Find the value of a and b. Leave your answers in simplest radical form.
For such questions, we should know the properties of right-angled triangle and isosceles triangle.
The long leg of a 30 - 60 - 90 is 18√3 units. Find the length of the hypotenuse.
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.
The long leg of a 30 - 60 - 90 is 18√3 units. Find the length of the hypotenuse.
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 y in this 45-45-90 triangle.
For such questions, we should know the properties of different triangles.
Calculate the length of y in this 45-45-90 triangle.
For such questions, we should know the properties of different triangles.
In this 45-45-90 triangle, I have been given the length of a leg. How do I find the length of the hypotenuse?
For such questions, we should know about the properties of right-angled and isosceles triangle.
In this 45-45-90 triangle, I have been given the length of a leg. How do I find the length of the hypotenuse?
For such questions, we should know about the properties of right-angled and isosceles triangle.
In this 45-45-90 triangle, I have been given a leg, so to find the other leg I...
We should know the properties of different triangles.
In this 45-45-90 triangle, I have been given a leg, so to find the other leg I...
We should know the properties of different triangles.
Find x.
For such questions, we should know the properties of both of isosceles triangle and right-angled triangle.
Find x.
For such questions, we should know the properties of both of isosceles triangle and right-angled triangle.
______ long is e.
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.
______ long is e.
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.
Side c is called _____________.
For such questions, we should know the properties of right-angled triangle.
Side c is called _____________.
For such questions, we should know the properties of right-angled triangle.
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 and trigonometric ratios.
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 and trigonometric ratios.
Determine the value of y.
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.
Determine the value of y.
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.
__________ is the opposite of squaring a number?
For such questions, we should know about different operations.
__________ is the opposite of squaring a number?
For such questions, we should know about different operations.
I have been given the long leg in this 30-60-90 triangle. Choose the correct way to find the short leg.
To solve such questions, we should know the properties of different triangles.
I have been given the long leg in this 30-60-90 triangle. Choose the correct way to find the short leg.
To solve such questions, we should know the properties of different triangles.
The side is the short leg of this 30-60-90 triangle is?
For such questions, we should know about different properties of different triangles.
The side is the short leg of this 30-60-90 triangle is?
For such questions, we should know about different properties of different triangles.
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.
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.
Find x.
For such questions, we should know the properties of triangles.
Find x.
For such questions, we should know the properties of triangles.
