Trigonometric ratios in right-angled trianglesIB MYP Maths Standard: Subtopic test

1. 1
   A ladder $5$ m long rests against a vertical wall on level ground. The foot of the ladder is $1.5$ m from the wall.

   (a)

   Find the angle the ladder makes with the ground.

   [1 mark]

   • A$17.5^\circ$
   • B$72.5^\circ$
   • C$16.7^\circ$
   • D$73.3^\circ$

   (b)

   How high up the wall does the ladder reach?

   [1 mark]

   • A$4.77$ m
   • B$3.50$ m
   • C$5.22$ m
   • D$1.50$ m

   (c)

   The foot of the ladder is moved so that it is $2$ m from the wall. Find the new angle between the ladder and the ground.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A hiker stands at the top of a vertical cliff that is $60$ m above the sea. She looks at a boat on the sea and measures the angle of depression of the boat as $25^\circ$.

   (a)

   What is the angle of elevation of the hiker from the boat?

   [1 mark]

   • A$65^\circ$
   • B$155^\circ$
   • C$115^\circ$
   • D$25^\circ$

   (b)

   How far is the boat from the foot of the cliff, to the nearest metre?

   [1 mark]

   • A$28$ m
   • B$142$ m
   • C$129$ m
   • D$54$ m

   (c)

   The boat sails $40$ m straight towards the cliff. Find the new angle of depression of the boat, to $1$ decimal place.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   In triangle $ABC$, angle $B=90^\circ$, $AB=7.2$ cm and $AC=11.5$ cm.

   (a)

   Find the size of angle $BAC$, to $1$ decimal place.

   [3 marks]

   (b)

   Find the length of $BC$ and the size of angle $ACB$.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A surveyor stands on level ground $45$ m from the foot of a vertical tower. Her eye is $1.6$ m above the ground. She measures the angle of elevation of the top of the tower as $38^\circ$, to the nearest degree.

   (a)

   (i) Find the height of the tower above the ground.
   (ii) Find the angle of depression of the surveyor's feet from the top of the tower, and explain why it is bigger than $38^\circ$.

   [6 marks]

   (b)

   A newspaper says that the tower is $40$ m tall. Use the fact that her angle is correct to the nearest degree to find the range of possible heights of the tower, and decide whether the newspaper's claim is consistent with her measurement. Explain one other source of error.

   [6 marks]

   Total for question 4: 12 marks

End of questions