TRIGONOMETRY AND PYTHAGORAS
TIP: When doing these sort of problems, remember:
a) When you see pictures of triangles in questions, you can normally find the answers by using sin, cos, tan or Pythagoras' theorem. Note that these fomulae only appy to right-angled triangles.
b) Always look to see if Pythagoras' Theorem can be used first (e.g. when are you given the lengths of 2 sides of a right-angled triangle) as these answers are the easiest to calulate.
c) It's crucial
that you remember that Cos involves the
line which is Close to the angle (adjacent)
and Sin involves the line which is Some
distance further away (opposite).
Solve the following:
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1. The diagram shows the cross-section of a house. The tip of the house roof is directly central. i) Calculate the length of the slope of the roof BC. ii) Explain two methods which can be used to determine the angle of slope xo. iii) Use one of your methods to find the angle xo. Give all answers to 3 significant figures. |
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2. The optimal angle for launching the rocket in the picture is 45o, how high should the tip of the rocket x be from the ground? Give your answer to 2 decimal places. |
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3. In a computer game, when the mouse arrow is clicked, the puppy will run towards it. The movement of the puppy is described in the computer program as being a horizontal movement followed by a vertical movement. The positions of the puppy and mouse are shown in the picture as (horizontal movement, vertical movement). To reach the arrow, at what angle from the horizontal must the puppy travel? (Give your answer to 2 d.p.)
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4. The diagram shows a bridge (not drawn to scale) with the following measurements: AC = 60m Calculate the distance AB and hence calculate the angle X. |
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5. Barnacle Bob looks over the cliff edge at a boat on the sea. He is able to measure the angle of despression as 50o. What is the distance of the boat from the cliff?
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6. Mountain rescue set off from base and walk 8km then 6km west before
finding the injured climber. They now need to find the quickest way
back to base. What bearing should they take (to the nearest degree)
?
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7. The diagram shows a prism wih a right angled triangle as its cross-section. The midpoint of line CD is indicated by M. Find the following lengths and angles: i) AC
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8. The diagram shows a cuboid. Find the length of the diagonal BH, when
BC = 1cm, CD = 2cm and DH = 3cm.
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