Question
Find a.
- 3
- 9
- 6
Hint:
We are given a right-angled triangle. We are given one of its angle. It is 60°. The other angle will be 30°. We are given the value of its hypotenuse. It is 18. We are asked to find the value of the other side. It is denoted by “a”.
The correct answer is: 9
Let the given triangle be ABC.
∠ABC = 90°
∠BAC = 60°
AB = a
BC = b
AC = 18
The sum of all angles of a triangle is 180°. Therefore, the remaining angle will be °
So, ∠ACB = 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. And the side opposite to 60° is BC.
Length of smallest side = a
Hypotenuse = 18
So we can write,
Hypotenuse = 2(length of smallest side)
AC = 2(AB)
18 = 2(a)
We will divide both the sides by 2 and rearrange the equation for “a”.
a = 18 ÷ 2
a = 9
Therefore, the value of a is 9.
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
If you are given the SHORT LEG of a 30-60-90 triangle, select the way to find the LONG LEG?
For such questions, we should know the properties of different triangles.
If you are given the SHORT LEG of a 30-60-90 triangle, select the way to find the LONG LEG?
For such questions, we should know the properties of different triangles.
If you are given the SHORT LEG of a 30-60-90 triangle, choose correct way to find the HYPOTENUSE.
For such questions, we should know the properties of different triangles
If you are given the SHORT LEG of a 30-60-90 triangle, choose correct way to find the HYPOTENUSE.
For such questions, we should know the properties of different triangles
Identify the type of triangle shown bellow.
For such questions, we should know the properties of a triangle.
Identify the type of triangle shown bellow.
For such questions, we should know the properties of a triangle.
If the leg of a 45-45-90 triangle is 7 cm long, then its hypotenuse is _____ cm.
For such questions, we should know the properties of different triangles.
If the leg of a 45-45-90 triangle is 7 cm long, then its hypotenuse is _____ cm.
For such questions, we should know the properties of different triangles.
Find the lengths of the other two sides of a right triangle if the length of the hypotenuse is 4√2 inches and one of the angles is 45∘.
For such questions, we should know the properties of different triangles.
Find the lengths of the other two sides of a right triangle if the length of the hypotenuse is 4√2 inches and one of the angles is 45∘.
For such questions, we should know the properties of different triangles.
Calculate the value of x.
For such questions, we should know the properties of right-angled triangle and isosceles triangle.
Calculate the value of x.
For such questions, we should know the properties of right-angled triangle and isosceles triangle.
Calculate the value of x.
For such questions, we should know properties of right-angled triangles.
Calculate the value of x.
For such questions, we should know properties of right-angled triangles.
Find b 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 b 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.
A square has diagonal length 13 m. Find the side length of the square, in centimeters, rounded to two decimal places.
For such questions, we should know the properties of triangle and square.
A square has diagonal length 13 m. Find the side length of the square, in centimeters, rounded to two decimal places.
For such questions, we should know the properties of triangle and square.
The length of side c is ____________
For such questions, we should know the properties of right-angled and isosceles triangle.
The length of side c is ____________
For such questions, we should know the properties of right-angled and isosceles 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.
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.
