Question
You are making a guitar pick that resembles an equilateral triangle with side lengths of 32 millimeters. The approximate height of the pick is?
- 32√3
- 16√3
- 32
- 16√2
Hint:
We are given that a guitar pick is a equilateral triangle. It has side 32mm. We are asked to find the height of the equilateral triangle. The height of any triangle is perpendicular drawn to its base. The triangle is ABC. The height is BD. We will use the properties of equilateral triangle and right-angled triangle to solve the question.
The correct answer is: 16√3
The triangle ABC is an equilateral triangle. Equilateral triangle has all sides same and the angles are 60°.
BD is the height. The height of equilateral triangle divides the base into two equal lengths.
We will consider the ∆BDC.
The angle BDC is 90°.
The length of the side BC is 32mm. It is the hypotenuse.
The length of the side DC is 16mm.
The angle BCD is 60°
The length of BD is given by the variable h.
We will use the trigonometric ratio.
For right-angled triangle, sine of an angle is the ratio of opposite side and hypotenuse. So, we will take the sine of angle BCD.
.
The value of altitude is 16√3.
For such questions, the properties of right-angled triangles are important. We should know about the trigonometric ratios. It includes sine, cosine, tangent etc.
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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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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.
