Introduction To Trigonometry Practice 3: Applications And Error Analysis

A ladder makes a $60^\circ$ angle with the ground and reaches a height of $6\sqrt{3}$ m. If the ladder length is $L$, which equation is correct?

Topic: Applications · Skill: Solve right-triangle numerical problems

A ramp is $10$ m long and makes a $30^\circ$ angle with the ground. What is its vertical height?

Topic: Applications · Skill: Solve right-triangle numerical problems

If $\tan A=\frac{5}{12}$ and the side adjacent to $A$ is $36$ cm, what is the side opposite $A$?

Topic: Ratio Evaluation · Skill: Find sides from a trigonometric ratio

In a right triangle, the sides are $9$, $12$, and $15$. If the selected angle has opposite side $9$, what is $\sec A$?

Topic: Ratio Evaluation · Skill: Find ratios from side lengths

A $3$-$4$-$5$ triangle and a $6$-$8$-$10$ triangle have the same acute angle opposite the shorter leg. What can be said about the sine of that angle?

Topic: Well-defined Ratios · Skill: Explain why trigonometric ratios depend on angle