Before the midterm

Confusing the sides of the triangle

The habit: Draw the triangle and label which distance is the hypotenuse and which is a leg before writing the relation.

9 practice questions are built to catch it, in 3 topics.

What it looks like

A question from related rates, with the answer this slip gives beside the right one.

Introductory2 marks · 2 min

A woman 1.5 m tall walks away from a 6 m lamppost along level ground. Let $x$ be her distance from the foot of the post and $s$ the length of her shadow, both changing with time. At one moment she is 12 m from the post. Which equation holds at every instant?

With the slip: $\displaystyle \dfrac{1.5}{s} = \dfrac{6}{x}$
Worked through: $\displaystyle \dfrac{1.5}{s} = \dfrac{6}{x + s}$

x ends at her feet, but the post’s triangle runs on to the tip of her shadow, which both triangles share. Its base is x + s.

See the worked solution

Where it comes up

Functions, graphs and inverses1 question
Implicit differentiation and inverse trigonometric functions1 question
Related rates7 questions

Practise against it

Each of these has an answer this slip gives. Work them on paper: if you fall into it, the verdict names it and the question comes back in review.

01
The angle $\theta$ satisfies $\sin\theta = \dfrac{2}{7}$ and $\dfrac{\pi}{2} < \theta < \pi$ . Find the exact value of $\tan\theta$ .
Functions, graphs and inversesStandard
02
Find the exact value of the expression below. $\displaystyle \cos\bigl(\arctan(-2)\bigr)$
Implicit differentiation and inverse trigonometric functionsStandard
03
A crate on a warehouse floor is dragged toward a wall by a rope tied to it at floor level. The rope runs up to a pulley fixed on the wall 3 m above the floor, and a winch hauls the rope in at 1 m/s. At what rate is the crate’s distance from the wall changing at the moment 5 m of rope lies between the pulley and the crate?
Related ratesStandard
04
A 3.4 m ladder leans against a vertical wall. Its foot slides away from the wall at 0.45 m/s. At what rate is the angle between the ladder and the ground changing at the moment the foot is 1.6 m from the wall?
Related ratesStandard
05
A 1.8 m tall person walks away from the base of a 5.4 m lamppost at 1.5 m/s along level ground. How fast is the tip of their shadow moving away from the lamppost?
Related ratesStandard
06
A camera on a tripod stands 0.4 km from a straight road. A car drives along the road at 1.5 km/min, moving away from the point on the road nearest the camera, and the camera turns to keep the car in frame. How fast is the camera rotating, in radians per minute, at the instant the car is 0.5 km from the camera?
Related ratesChallenging

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