Question

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

Answer 1

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.