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If $\triangle ABC \sim \triangle DEF$ and $\frac{AB}{DE} = \frac{2}{3}$, what is the ratio of $\frac{BC}{EF}$?

Which of the following statements is true regarding similar triangles?

In a right-angled triangle, what is the ratio that defines the sine of an angle $\theta$?

Which trigonometric ratio is the reciprocal of $\sin \theta$?

What is the value of $\cos 60^\circ$?

In a right triangle, if the opposite side to an angle $\theta$ is 5 and the hypotenuse is 13, what is $\sin \theta$?

If $\tan \theta = 1$ and $0^\circ < \theta < 90^\circ$, what is the measure of angle $\theta$?

What is the value of $\sin 30^\circ + \cos 60^\circ$?

In the Cartesian plane, an angle $\theta$ has its terminal arm in Quadrant II. Which trigonometric ratio is positive in this quadrant?

An observer looks up at a bird at an angle of elevation of $30^\circ$. If the bird is 10 meters above the observer's horizontal line of sight, what is the horizontal distance between the observer and the bird?

If $\cos \theta = \frac{1}{3}$, find the value of $\sin^2 \theta + \cos^2 \theta$.

Given $\triangle ABC$ is a right-angled triangle with $\angle C = 90^\circ$, $AB = 10$, and $BC = 5$, find the value of $\tan A$.

If $\sin \theta = \frac{3}{5}$ and $\theta$ is in the second quadrant, what is the value of $\cos \theta$?

A ladder leans against a wall, making an angle of $60^\circ$ with the ground. The foot of the ladder is 2 meters away from the wall. How far up the wall does the ladder reach?

What is the exact value of$\sin(22.5^\circ)$?

Two similar triangles, $\triangle ABC$ and $\triangle DEF$, have areas of $16 \text{ cm}^2$ and $25 \text{ cm}^2$ respectively. If $AB = 4 \text{ cm}$, what is the length of $DE$?

Given that $\cos(x) = \frac{1}{7}$ and $\cos(y) = \frac{13}{14}$, where $x$ and $y$ are acute angles, what is the value of $\cos(x - y)$?

Determine the number of solutions to the equation $\sin(x) = \frac{x}{100}$

Consider a triangle in the Cartesian plane with vertices at (0, 0), (5, 0), and (0, 12). What is the sine of the angle at the origin?

A tower casts a shadow of 30 meters when the angle of elevation of the sun is 60°. What is the height of the tower?

In a $30^\circ$-$60^\circ$-$90^\circ$ triangle, what is the ratio of the side opposite to $30^\circ$ to the hypotenuse?

In which quadrant of the Cartesian plane is $ an heta$ positive and $\cos heta$ negative?

Consider two similar triangles $ riangle ABC$ and $ riangle DEF$. If the ratio of their corresponding heights is $3:5$, what is the ratio of their areas?

If in $ riangle ABC$ and $ riangle DEF$, $\angle A = \angle D$ and $\angle B = \angle E$, and $AB = 2DE$, what is the ratio of the area of $ riangle ABC$ to the area of $ riangle DEF$?

Given that $\sin x = \cos y$ for acute angles $x$ and $y$, what can be concluded about the relationship between $x$ and $y$?

If two triangles are similar, which of the following statements about their corresponding angles is always true?

In a right-angled triangle $ABC$, where $C$ is the right angle, which side is the hypotenuse?

What is the relationship between $an heta$ and $\cot heta$?

In which quadrant of the Cartesian plane are both sine and cosine negative?

A surveyor measures the angle of elevation to the top of a building to be $25^\circ$. If the surveyor is standing 50 meters from the base of the building, approximately how tall is the building?

Given that $ext{cosec } heta = 2$, what is the value of $\sin heta$?

What is the value of $\sin^2(45^\circ) + \cos^2(45^\circ)$?

If a right triangle has legs of length 3 and 4, what is the cosine of the angle opposite the side of length 3?

Two buildings are 50 meters apart. The angle of depression from the top of the taller building to the top of the shorter building is $20^\circ$. If the taller building is 70 meters tall, how tall is the shorter building?

Given a triangle $ABC$ with sides $a$, $b$, and $c$ opposite to angles $A$, $B$, and $C$ respectively, and given that $a = 10$, $b = 12$, and $C = 60^\circ$, find the length of side $c$.

If $ \triangle PQR \sim \triangle XYZ $ and $ \frac{PQ}{XY} = \frac{5}{7} $, what is the value of $ \frac{PR}{XZ} $?

In a right triangle, which trigonometric ratio represents the relationship between the adjacent side and the hypotenuse?

If $ \tan(\theta) = \frac{4}{3} $, what is the value of $ \cot(\theta) $?

Given $ \triangle ABC \sim \triangle MNP $, which of the following statements must be true?

In a right triangle $ ABC $ with right angle at $ C $, if $ AB = 13 $ and $ BC = 5 $, find $ \cos A $.

If an angle $ \theta $ in the Cartesian plane has its terminal arm in Quadrant III, which of the following is true?

A ladder 6 meters long leans against a wall, making an angle of 75° with the ground. How high up the wall does the ladder reach?

Given that $ \sin \theta = \frac{1}{2} $ and $ 0^\circ < \theta < 90^\circ $, what is the value of $ \cos \theta $?

If $ \cos(\theta) = \frac{5}{13} $ and $ \theta $ is in the fourth quadrant, what is $ \tan(\theta) $?

An observer stands 50 meters away from a building and observes the top of the building at an angle of elevation of $30^\circ$. What is the height of the building?

What is the exact value of $ \cos 15^\circ $?

Given $ \sin x = \frac{1}{\sqrt{5}} $ and $ \cos y = \frac{2}{\sqrt{5}} $, where both $ x $ and $ y $ are acute angles, find the value of $ \sin(x + y) $.

In triangle $ ABC $, $ a = 5 $, $ b = 7 $, and $ \angle C = 60^\circ $. Find the length of side $ c $.

What is the range of the function $ f(x) = 3 \sin(2x) + 1 $?

Consider the function $ f(x) = \frac{\sin x}{x} $ for $ x > 0 $. What value does $ f(x) $ approach as $ x $ approaches infinity?

Find the exact value of $ \tan(\frac{5\pi}{12}) $.

Given a regular hexagon inscribed in a circle of radius 1, what is the value of the product of the distances from one vertex to all other vertices?