Applications of right-angled trigonometry Quiz

1. A ladder $5$ m long leans against a wall and makes an angle of $70^\circ$ with the ground. How high up the wall does it reach?

• A. $1.71$ m
• B. $4.70$ m
• C. $13.7$ m
• D. $1.82$ m

2. From the top of a $30$ m tower, the angle of depression of a boat is $25^\circ$. How far is the boat from the foot of the tower?

• A. $64.3$ m
• B. $14.0$ m
• C. $12.7$ m
• D. $71.0$ m

3. A cuboid measures $4$ cm by $3$ cm by $12$ cm. What is the length of its space diagonal?

• A. $13$ cm
• B. $19$ cm
• C. $169$ cm
• D. $15$ cm

4. A plane flies $100$ km on a bearing of $120^\circ$. How far south of its start is it?

• A. $86.6$ km
• B. $100$ km
• C. $50$ km
• D. $173$ km

5. A rule says a ramp must not rise at more than $5^\circ$. What is the greatest whole number of cm of height it can gain over a horizontal distance of $500$ cm?

• A. $44$ cm
• B. $42$ cm
• C. $50$ cm
• D. $43$ cm