Right Triangles - Math

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Question

In this figure, , $Y=6$\sqrt{3}$$ , and . What is the value of angle ?

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Answer

Notice that these sides fit the pattern of a 30:60:90 right triangle: $x:x$\sqrt{3}$:2x$ .

In this case, .

Since angle is opposite , it must be $30^\circ$ .

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Question

A triangle has angles of $30^\circ:60^\circ:90^\circ$ . If the side opposite the $30^\circ$ angle is , what is the length of the side opposite $60^\circ$ ?

Tap to reveal answer

Answer

The pattern for $30^\circ:60^\circ:90^\circ$ is that the sides will be $x:x$\sqrt{3}$:2x$ .

If the side opposite $30^\circ$ is , then the side opposite $60^\circ$ will be $7$\sqrt{3}$$ .

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Question

Let ABC be a right triangle with sides = 3 inches, = 4 inches, and = 5 inches. In degrees, what is the $\sin \Theta$ where $\Theta$ is the angle opposite of side ?

Tap to reveal answer

Answer

We are looking for $\sin(\theta )$ . Remember the definition of in a right triangle is the length of the opposite side divided by the length of the hypotenuse.

So therefore, without figuring out $\Theta$ we can find

$\sin \Theta =\frac{3}{5}$=.6$

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Question

In this figure, if angle $c=90^\circ$ , side , and side , what is the measure of angle ?

Tap to reveal answer

Answer

Since $c=90^\circ$ , we know we are working with a right triangle.

That means that $\sin(\theta)=\frac{\text{opposite}$}{$\text{hypotenuse}$}$ .

In this problem, that would be:

$\sin(a)=\frac{\text{Z}$}{$\text{X}$}$

Plug in our given values:

$\sin(a)=\frac{8}{12}$$

$\sin(a)=\frac{2}{3}$$

$a=41.8^\circ$

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Question

In this figure, side , , and $c=90^\circ$ . What is the value of angle ?

Tap to reveal answer

Answer

Since $c=90^\circ$ , we know we are working with a right triangle.

That means that $\cos(\theta)=\frac{\text{adjacent}$}{$\text{hypotenuse}$}$ .

In this problem, that would be:

$\cos(a)=\frac{\text{Y}$}{$\text{X}$}$

Plug in our given values:

$\cos(a)=\frac{\text{13}$}{$\text{20}$}$

$\cos(a)=0.65$

$a=49.46^\circ$

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Question

Let ABC be a right triangle with sides = 3 inches, = 4 inches, and = 5 inches. In degrees, what is the $\sin \Theta$ where $\Theta$ is the angle opposite of side ?

Tap to reveal answer

Answer

We are looking for $\sin(\theta )$ . Remember the definition of in a right triangle is the length of the opposite side divided by the length of the hypotenuse.

So therefore, without figuring out $\Theta$ we can find

$\sin \Theta =\frac{3}{5}$=.6$

← Didn't Know|Knew It →

Question

In this figure, if angle $c=90^\circ$ , side , and side , what is the measure of angle ?

Tap to reveal answer

Answer

Since $c=90^\circ$ , we know we are working with a right triangle.

That means that $\sin(\theta)=\frac{\text{opposite}$}{$\text{hypotenuse}$}$ .

In this problem, that would be:

$\sin(a)=\frac{\text{Z}$}{$\text{X}$}$

Plug in our given values:

$\sin(a)=\frac{8}{12}$$

$\sin(a)=\frac{2}{3}$$

$a=41.8^\circ$

← Didn't Know|Knew It →

Question

In this figure, side , , and $c=90^\circ$ . What is the value of angle ?

Tap to reveal answer

Answer

Since $c=90^\circ$ , we know we are working with a right triangle.

That means that $\cos(\theta)=\frac{\text{adjacent}$}{$\text{hypotenuse}$}$ .

In this problem, that would be:

$\cos(a)=\frac{\text{Y}$}{$\text{X}$}$

Plug in our given values:

$\cos(a)=\frac{\text{13}$}{$\text{20}$}$

$\cos(a)=0.65$

$a=49.46^\circ$

← Didn't Know|Knew It →

Question

In this figure, , $Y=6$\sqrt{3}$$ , and . What is the value of angle ?

Tap to reveal answer

Answer

Notice that these sides fit the pattern of a 30:60:90 right triangle: $x:x$\sqrt{3}$:2x$ .

In this case, .

Since angle is opposite , it must be $30^\circ$ .

← Didn't Know|Knew It →

Question

A triangle has angles of $30^\circ:60^\circ:90^\circ$ . If the side opposite the $30^\circ$ angle is , what is the length of the side opposite $60^\circ$ ?

Tap to reveal answer

Answer

The pattern for $30^\circ:60^\circ:90^\circ$ is that the sides will be $x:x$\sqrt{3}$:2x$ .

If the side opposite $30^\circ$ is , then the side opposite $60^\circ$ will be $7$\sqrt{3}$$ .

← Didn't Know|Knew It →

Question

Let ABC be a right triangle with sides = 3 inches, = 4 inches, and = 5 inches. In degrees, what is the $\sin \Theta$ where $\Theta$ is the angle opposite of side ?

Tap to reveal answer

Answer

We are looking for $\sin(\theta )$ . Remember the definition of in a right triangle is the length of the opposite side divided by the length of the hypotenuse.

So therefore, without figuring out $\Theta$ we can find

$\sin \Theta =\frac{3}{5}$=.6$

← Didn't Know|Knew It →

Question

In this figure, if angle $c=90^\circ$ , side , and side , what is the measure of angle ?

Tap to reveal answer

Answer

Since $c=90^\circ$ , we know we are working with a right triangle.

That means that $\sin(\theta)=\frac{\text{opposite}$}{$\text{hypotenuse}$}$ .

In this problem, that would be:

$\sin(a)=\frac{\text{Z}$}{$\text{X}$}$

Plug in our given values:

$\sin(a)=\frac{8}{12}$$

$\sin(a)=\frac{2}{3}$$

$a=41.8^\circ$

← Didn't Know|Knew It →

Question

In this figure, side , , and $c=90^\circ$ . What is the value of angle ?

Tap to reveal answer

Answer

Since $c=90^\circ$ , we know we are working with a right triangle.

That means that $\cos(\theta)=\frac{\text{adjacent}$}{$\text{hypotenuse}$}$ .

In this problem, that would be:

$\cos(a)=\frac{\text{Y}$}{$\text{X}$}$

Plug in our given values:

$\cos(a)=\frac{\text{13}$}{$\text{20}$}$

$\cos(a)=0.65$

$a=49.46^\circ$

← Didn't Know|Knew It →

Question

In this figure, , $Y=6$\sqrt{3}$$ , and . What is the value of angle ?

Tap to reveal answer

Answer

Notice that these sides fit the pattern of a 30:60:90 right triangle: $x:x$\sqrt{3}$:2x$ .

In this case, .

Since angle is opposite , it must be $30^\circ$ .

← Didn't Know|Knew It →

Question

A triangle has angles of $30^\circ:60^\circ:90^\circ$ . If the side opposite the $30^\circ$ angle is , what is the length of the side opposite $60^\circ$ ?

Tap to reveal answer

Answer

The pattern for $30^\circ:60^\circ:90^\circ$ is that the sides will be $x:x$\sqrt{3}$:2x$ .

If the side opposite $30^\circ$ is , then the side opposite $60^\circ$ will be $7$\sqrt{3}$$ .

← Didn't Know|Knew It →

Question

Let ABC be a right triangle with sides = 3 inches, = 4 inches, and = 5 inches. In degrees, what is the $\sin \Theta$ where $\Theta$ is the angle opposite of side ?

Tap to reveal answer

Answer

We are looking for $\sin(\theta )$ . Remember the definition of in a right triangle is the length of the opposite side divided by the length of the hypotenuse.

So therefore, without figuring out $\Theta$ we can find

$\sin \Theta =\frac{3}{5}$=.6$

← Didn't Know|Knew It →

Question

In this figure, if angle $c=90^\circ$ , side , and side , what is the measure of angle ?

Tap to reveal answer

Answer

Since $c=90^\circ$ , we know we are working with a right triangle.

That means that $\sin(\theta)=\frac{\text{opposite}$}{$\text{hypotenuse}$}$ .

In this problem, that would be:

$\sin(a)=\frac{\text{Z}$}{$\text{X}$}$

Plug in our given values:

$\sin(a)=\frac{8}{12}$$

$\sin(a)=\frac{2}{3}$$

$a=41.8^\circ$

← Didn't Know|Knew It →

Question

In this figure, side , , and $c=90^\circ$ . What is the value of angle ?

Tap to reveal answer

Answer

Since $c=90^\circ$ , we know we are working with a right triangle.

That means that $\cos(\theta)=\frac{\text{adjacent}$}{$\text{hypotenuse}$}$ .

In this problem, that would be:

$\cos(a)=\frac{\text{Y}$}{$\text{X}$}$

Plug in our given values:

$\cos(a)=\frac{\text{13}$}{$\text{20}$}$

$\cos(a)=0.65$

$a=49.46^\circ$

← Didn't Know|Knew It →

Question

In this figure, , $Y=6$\sqrt{3}$$ , and . What is the value of angle ?

Tap to reveal answer

Answer

Notice that these sides fit the pattern of a 30:60:90 right triangle: $x:x$\sqrt{3}$:2x$ .

In this case, .

Since angle is opposite , it must be $30^\circ$ .

← Didn't Know|Knew It →

Question

A triangle has angles of $30^\circ:60^\circ:90^\circ$ . If the side opposite the $30^\circ$ angle is , what is the length of the side opposite $60^\circ$ ?

Tap to reveal answer

Answer

The pattern for $30^\circ:60^\circ:90^\circ$ is that the sides will be $x:x$\sqrt{3}$:2x$ .

If the side opposite $30^\circ$ is , then the side opposite $60^\circ$ will be $7$\sqrt{3}$$ .

← Didn't Know|Knew It →

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