Trigonometry

Hong Kong

Stage 1 - Stage 3

A soft drink can has a height of $13$13 cm and a radius of $3$3 cm. Find $L$`L`, the length of the longest straw that can fit into the can (so that the straw is not bent and fits entirely inside the can).

Give your answer rounded *down* to the nearest cm, to ensure it fits inside the can.

Easy

Approx 2 minutes

The final approach of an aeroplane when landing requires the pilot to adjust their angle of descent to about $3$3°. If the plane is $12$12 metres above the runway and has $d$`d` metres until touchdown, find $d$`d` to the nearest metre.

Two flag posts of height $13$13 m and $18$18 m are erected $21$21 m apart. Find $l$`l`, the length of the string (in metres) needed to join the tops of the two posts, correct to one decimal place.

A suspension bridge is being built. The top of the concrete tower is $35.5$35.5 metres above the bridge and the connection point for the main cable is $65.9$65.9 metres from the tower.

Assume that the concrete tower and the bridge are perpendicular to each other.

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