For this triangle find the value of trigonometric ratio $\tan C$. Simplify your fractions where necessary.

 

Explain why $\cos B=\sin C$ and $\sin B=\cos C$.

A ladder is leaning against a wall. The ladder has a known length of $3 \mathrm{m}$. Cassandra wishes to find the vertical height to which the ladder reaches but she has only $15 \mathrm{cm}$ ruler. She measures a distance of $15 \mathrm{cm}$ up the ladder and drops a piece of string to the ground. She measures the length of the string to be $10.6 \mathrm{cm}$.

From the information, determine the vertical height(in cm) to which the ladder reaches.

In physics, when an object travels at an angle, it is easier to break up the motion into a horizontal component and vertical component. The principles of physics can then be applied to both directions. Suppose an object travels with a velocity(speed) of $25 \mathrm{m}/\mathrm{s}$ at an angle of $40$ degrees with the ground. Find the horizontal and vertical components of the object's velocity?

Explain how the diagram below can be used to prove Pythagoras' theorem.

Is the following pair of triangles similar? If so, find the similarity postulate used.

Is the following pair of triangles similar? If so, find the similarity postulate used.

Is the following pair of triangles similar? If so, find the similarity postulate used.

Is the following pair of triangles similar? If so, find the similarity postulate used.