How to find the height of an eqilateral triangle - ISEE Upper Level Quantitative Reasoning

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Question

The length of one side of an equilateral triangle is 4 centimeters. Give the height (altitude) of the triangle.

Answer

$Area=\frac{1}{2}absinC$ ,

where and are the lengths of two sides and is the corresponding angle.

In an equilateral triangle, all of the sides have the same length, and all three angles are $60^{\circ}$ .

$Area=\frac{1}{2}absinC=\frac{1}{2}\times 4\times 4\times sin60^{\circ}$

$sin60^{\circ}=\frac{\sqrt{3}}{2}\Rightarrow Area=\frac{1}{2}\times 4\times 4\times \frac{\sqrt{3}}{2}=4\sqrt{3}\ cm^2$

Now plug this area into the alternate formula for the area of the triangle and solve for the height:

$Area =\frac{bh}2{}\Rightarrow 4\sqrt{3}=\frac{4\times h}{2}\Rightarrow h=2\sqrt{3}\ cm$

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Question

The height of the equilateral triangle below is 5 centimeters. Give the perimeter of the triangle.

Answer

In an equilateral triangle all of the sides have the same length, so all we need to do is find the length of one side.

We know that, in an equilateral triangle, all three angles measure $60^{\circ}$ .

$sin\angle A=\frac{h}{AB}=\frac{h}{c}$

$sin\angle A=\frac{h}{c}\Rightarrow sin60^{\circ}=\frac{4}{c}\Rightarrow \frac{\sqrt{3}}{2}=\frac{4}{c}\Rightarrow c=\frac{8}{\sqrt{3}}=\frac{8\sqrt{3}}{3} \ cm$

Compare your answer with the correct one above

Question

The length of one side of an equilateral triangle is 4 centimeters. Give the height (altitude) of the triangle.

Answer

$Area=\frac{1}{2}absinC$ ,

where and are the lengths of two sides and is the corresponding angle.

In an equilateral triangle, all of the sides have the same length, and all three angles are $60^{\circ}$ .

$Area=\frac{1}{2}absinC=\frac{1}{2}\times 4\times 4\times sin60^{\circ}$

$sin60^{\circ}=\frac{\sqrt{3}}{2}\Rightarrow Area=\frac{1}{2}\times 4\times 4\times \frac{\sqrt{3}}{2}=4\sqrt{3}\ cm^2$

Now plug this area into the alternate formula for the area of the triangle and solve for the height:

$Area =\frac{bh}2{}\Rightarrow 4\sqrt{3}=\frac{4\times h}{2}\Rightarrow h=2\sqrt{3}\ cm$

Compare your answer with the correct one above

Question

The height of the equilateral triangle below is 5 centimeters. Give the perimeter of the triangle.

Answer

In an equilateral triangle all of the sides have the same length, so all we need to do is find the length of one side.

We know that, in an equilateral triangle, all three angles measure $60^{\circ}$ .

$sin\angle A=\frac{h}{AB}=\frac{h}{c}$

$sin\angle A=\frac{h}{c}\Rightarrow sin60^{\circ}=\frac{4}{c}\Rightarrow \frac{\sqrt{3}}{2}=\frac{4}{c}\Rightarrow c=\frac{8}{\sqrt{3}}=\frac{8\sqrt{3}}{3} \ cm$

Compare your answer with the correct one above

Question

The length of one side of an equilateral triangle is 4 centimeters. Give the height (altitude) of the triangle.

Answer

$Area=\frac{1}{2}absinC$ ,

where and are the lengths of two sides and is the corresponding angle.

In an equilateral triangle, all of the sides have the same length, and all three angles are $60^{\circ}$ .

$Area=\frac{1}{2}absinC=\frac{1}{2}\times 4\times 4\times sin60^{\circ}$

$sin60^{\circ}=\frac{\sqrt{3}}{2}\Rightarrow Area=\frac{1}{2}\times 4\times 4\times \frac{\sqrt{3}}{2}=4\sqrt{3}\ cm^2$

Now plug this area into the alternate formula for the area of the triangle and solve for the height:

$Area =\frac{bh}2{}\Rightarrow 4\sqrt{3}=\frac{4\times h}{2}\Rightarrow h=2\sqrt{3}\ cm$

Compare your answer with the correct one above

Question

The height of the equilateral triangle below is 5 centimeters. Give the perimeter of the triangle.

Answer

In an equilateral triangle all of the sides have the same length, so all we need to do is find the length of one side.

We know that, in an equilateral triangle, all three angles measure $60^{\circ}$ .

$sin\angle A=\frac{h}{AB}=\frac{h}{c}$

$sin\angle A=\frac{h}{c}\Rightarrow sin60^{\circ}=\frac{4}{c}\Rightarrow \frac{\sqrt{3}}{2}=\frac{4}{c}\Rightarrow c=\frac{8}{\sqrt{3}}=\frac{8\sqrt{3}}{3} \ cm$

Compare your answer with the correct one above

Question

The length of one side of an equilateral triangle is 4 centimeters. Give the height (altitude) of the triangle.

Answer

$Area=\frac{1}{2}absinC$ ,

where and are the lengths of two sides and is the corresponding angle.

In an equilateral triangle, all of the sides have the same length, and all three angles are $60^{\circ}$ .

$Area=\frac{1}{2}absinC=\frac{1}{2}\times 4\times 4\times sin60^{\circ}$

$sin60^{\circ}=\frac{\sqrt{3}}{2}\Rightarrow Area=\frac{1}{2}\times 4\times 4\times \frac{\sqrt{3}}{2}=4\sqrt{3}\ cm^2$

Now plug this area into the alternate formula for the area of the triangle and solve for the height:

$Area =\frac{bh}2{}\Rightarrow 4\sqrt{3}=\frac{4\times h}{2}\Rightarrow h=2\sqrt{3}\ cm$

Compare your answer with the correct one above

Question

The height of the equilateral triangle below is 5 centimeters. Give the perimeter of the triangle.

Answer

In an equilateral triangle all of the sides have the same length, so all we need to do is find the length of one side.

We know that, in an equilateral triangle, all three angles measure $60^{\circ}$ .

$sin\angle A=\frac{h}{AB}=\frac{h}{c}$

$sin\angle A=\frac{h}{c}\Rightarrow sin60^{\circ}=\frac{4}{c}\Rightarrow \frac{\sqrt{3}}{2}=\frac{4}{c}\Rightarrow c=\frac{8}{\sqrt{3}}=\frac{8\sqrt{3}}{3} \ cm$

Compare your answer with the correct one above

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How to find the height of an eqilateral triangle - ISEE Upper Level Quantitative Reasoning

The length of one side of an equilateral triangle is 4 centimeters. Give the height (altitude) of the triangle.

, where and are the lengths of two sides and is the corresponding angle. In an equilateral triangle, all of the sides have the same length, and all three angles are . Now plug this area into the alternate formula for the area of the triangle and solve for the height:

The height of the equilateral triangle below is 5 centimeters. Give the perimeter of the triangle.

In an equilateral triangle all of the sides have the same length, so all we need to do is find the length of one side. We know that, in an equilateral triangle, all three angles measure .

The length of one side of an equilateral triangle is 4 centimeters. Give the height (altitude) of the triangle.

, where and are the lengths of two sides and is the corresponding angle. In an equilateral triangle, all of the sides have the same length, and all three angles are . Now plug this area into the alternate formula for the area of the triangle and solve for the height:

The height of the equilateral triangle below is 5 centimeters. Give the perimeter of the triangle.

In an equilateral triangle all of the sides have the same length, so all we need to do is find the length of one side. We know that, in an equilateral triangle, all three angles measure .

The length of one side of an equilateral triangle is 4 centimeters. Give the height (altitude) of the triangle.

, where and are the lengths of two sides and is the corresponding angle. In an equilateral triangle, all of the sides have the same length, and all three angles are . Now plug this area into the alternate formula for the area of the triangle and solve for the height:

The height of the equilateral triangle below is 5 centimeters. Give the perimeter of the triangle.

In an equilateral triangle all of the sides have the same length, so all we need to do is find the length of one side. We know that, in an equilateral triangle, all three angles measure .

The length of one side of an equilateral triangle is 4 centimeters. Give the height (altitude) of the triangle.

, where and are the lengths of two sides and is the corresponding angle. In an equilateral triangle, all of the sides have the same length, and all three angles are . Now plug this area into the alternate formula for the area of the triangle and solve for the height:

The height of the equilateral triangle below is 5 centimeters. Give the perimeter of the triangle.

In an equilateral triangle all of the sides have the same length, so all we need to do is find the length of one side. We know that, in an equilateral triangle, all three angles measure .