3.3 Applications of trigonometry Quiz

1. From 25 m away, the angle of elevation of the top of a tree is $45^\circ$. How tall is the tree?

• A. $25\sqrt2$ m
• B. $25$ m
• C. $12.5$ m
• D. $\frac{25}{\sqrt2}$ m

2. The bearing of $Y$ from $X$ is $215^\circ$. Find the bearing of $X$ from $Y$.

• A. $035^\circ$
• B. $145^\circ$
• C. $395^\circ$
• D. $125^\circ$

3. From the top of a 30 m cliff, the angle of depression of a boat is $30^\circ$. How far is the boat from the foot of the cliff?

• A. $10\sqrt3$ m
• B. $15$ m
• C. $30\sqrt3$ m
• D. $60$ m

4. A hiker walks 8 km north then 6 km east. How far is she from her start?

• A. $14$ km
• B. $10$ km
• C. $\sqrt{28}$ km
• D. $2$ km

5. A hiker walks 8 km north then 6 km east. Find the bearing of her position from the start, to the nearest degree.

• A. $037^\circ$
• B. $053^\circ$
• C. $323^\circ$
• D. $090^\circ$