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Can someone please help me with question 4 and 5. I’ve been having so much trouble we these type of questions. Thank you!

Can someone please help me with question 4 and 5. I’ve been having so much trouble-example-1
User Abdolence
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Answer:

question 4:

the smaller building is 262.31 metres tall

Explanation:

see the diagram attached:

1. draw a diagram:

  • as ive done below, it is easiest to solve this type of equation if you draw it out as a diagram

2. as you can see in the diagram, a right angled triangle has been created.

  • assuming you understand basic trigonometry, you will see that as we know 1 angle (3 degrees, 21 minutes), and 1 side length (46m), we can now solve for the other sides, which is what the question is asking us to do.
  • the side length we have been given (46m) is opposite the right angle (90°) and is the longest side of the triangle, making it the hypotenuse. So we know:
  • hypotenuse = 46m

  • as we are trying to find the difference between the heights of the buildings, we are trying to find the side opposite the given angle (3°21'). As it is opposite from the given angle, it is referred to in trigonometry as the opposite. As we don't yet know the length of the Opposite, i have labelled it x in the diagram.
  • known angle = 3°21'
  • opposite = x

3. convert the known angle from degrees and minutes to degrees.

  • 3 degrees 21 minutes =
  • 3 degrees + 21 minutes (there are 60 minutes in a degree, so to convert the 21 minutes into degrees, divide 21 by 60)
  • 21 minutes / 60 = 0.35 degrees

4. Identify which trigonometry ratio to use:

sin =
(opposite)/(hypotenuse)

cos =
(adjacent)/(hypotenuse)

tan =
(opposite)/(adjacent)

  • as we know the hypotenuse, and we want to know the opposite, the will use Sin.

5. insert known values into the equation:

  • sin θ
    (opposite)/(hypotenuse)
  • we know the hypotenuse = 46
  • we know the given angle = 3.35°
  • we have labelled the opposite side x
  • therefore our new equation looks like:
  • sin (3.35) =
    (x)/(46)
  • as we know the denominator (bottom value of the fraction), we multiply it by the angle to find the length of the unknown side (x):
  • 46 x sin (3.35) = 2.688 (use a calculator for this step)
  • we now know the length of the unknown side (x):
  • x = 2.688 metres

6. Interpreting the question with new knowledge:

  • as can be seen in the diagram, the unknown side (x), was the difference between the heights of the building.
  • we can now replace side x with 2.688
  • To find the height of building 2, simply subtract the difference between the buildings (2.688m), from the height of the tallest building (265m) to find the height of the smallest building.
  • 265 - 2.688 = 262.312 m (height of building 2)
  • the question says only to 2 decimal places so we can round the height to 262.31 metres.

the height of building 2 is 262.31 metres.

User Donovan Charpin
by
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