Angles of elevation & depression

In this part of the question, you will be assessed on the quality of your organisation, communication and accuracy in writing.

How much would be saved per week if the 8 street lights were only on from 7 p.m. to 5 a.m.? Give your answer in pounds, correct to the nearest penny.

You must show all your working.

A lamp post is vertical and stands on horizontal ground. The angle of elevation of the top of the lamp post is 68° when measured from a point 3. 3 m from the centre of the base of the lamp post.

Calculate the height of the lamp post.

A forest of trees absorbs 2·3 × 10¹¹ grams of carbon dioxide per year. Which of the following is 2·3 × 10¹¹?

Circle your answer.

230 000 000 000 23 000 000 000 2 300 000 000 000

0·000 000 000 002 3 0·000 000 000 023

A report states that a fire in a forest has a high risk of spreading when there are more than 60 trees per acre.

There are 615 trees in Grancwm Forest. The forest covers an area of 40 000 m².

Would a fire in Grancwm Forest have a high risk of spreading?

You must show all your working to support your answer.

Show that the pine tree has a vertical height of 17 metres.

A cylindrical log is cut from this pine tree. The circumference of the cross-section of the log is 1·75 m. The length of the log is half the height of the tree.

Calculate the volume of the log. Give your answer in m³.

You must show all your working.

Volume of the log is_{…………………........ ……} m³

Llinos walks to the summit of Snowdon, passing the lake called Llyn Glaslyn.

Her height above sea level increases by 485 m from Llyn Glaslyn to the summit.

From the summit, she sees two small boats on Llyn Glaslyn. Both boats are in the same direction from the summit. The angles of depression of the two boats are 41º and 27º, as shown in the diagram.

Calculate the distance between the boats.

The diagram below is a sketch of the Eiffel Tower.

The sketch is drawn to scale. The Eiffel Tower is 324 metres tall. Visitors can climb up to the Level 2 viewing platform using the internal steps.

Which of the following is a reasonable estimate of the number of steps from the ground to

the Level 2 viewing platform?

150 650 2500 3500 6500

Calculate the angle of elevation of the top of the Eiffel Tower from the point P.

The diagram below is a sketch of the Eiffel Tower.

The sketch is drawn to scale. The Eiffel Tower is 324 metres tall. Visitors can climb up to the Level 2 viewing platform using the internal steps.

Which of the following is a reasonable estimate of the number of steps from the ground to

the Level 2 viewing platform?

150 650 2500 3500 6500

Calculate the angle of elevation of the top of the Eiffel Tower from the point P.

Ursula is lying on her surfboard 180 metres away from the foot of a vertical cliff. The height of the cliff is 146 metres.

Ursula was told that if the angle of elevation of the top of the cliff from her lying position is between 42° and 45°, it is safe for her to attempt to stand on her surfboard. Calculate the angle of elevation of the top of the cliff from Ursula’s position lying on her surfboard. State whether it is • safe for Ursula to attempt to stand, or • not safe as she is too near the cliff, or

• not safe as she is too far out at sea.

Ursula is lying on her surfboard 180 metres away from the foot of a vertical cliff. The height of the cliff is 146 metres.

Ursula was told that if the angle of elevation of the top of the cliff from her lying position is between 42° and 45°, it is safe for her to attempt to stand on her surfboard. Calculate the angle of elevation of the top of the cliff from Ursula’s position lying on her surfboard. State whether it is • safe for Ursula to attempt to stand, or • not safe as she is too near the cliff, or

• not safe as she is too far out at sea.

Gwenda enjoys road running.

In this part of the question, you will be assessed on the quality of your organisation, communication and accuracy in writing.

She keeps a record of her run each day this week.

Last week, her average speed for the week was 9.6 kilometres per hour. Calculate Gwenda’s percentage improvement in her average speed from last week to this week.

You must show all your working.

Percentage improvement is_{…………........ …………} %

The diagram shows the cross-section of one part of her run.

Calculate the angle of elevation of the road.

Gwenda runs on another section of uneven road from A to B. The rise in this section of the road is 300 metres. The angle of elevation of B from A is 10°.

Calculate an estimate of how far Gwenda has run.

State any assumption you have made.

What is the impact of your assumption on your answer?