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A ladder resting on a vertical wall makes an angle whose tangent is 2…

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A ladder resting on a vertical wall makes an angle whose tangent is 2.4 with the ground. If the distance between the foot of the ladder and the wall is 50cm, what is the length of the ladder?

A. 1.2m

B. 9m

C. 1.3m

D. 1m

QUICK ANSWER…

C

DETAILS…

We would have to sketch this to know exactly what we’re dealing with…

A ladder resting on a vertical wall makes an angle whose tangent is 2

From the question, tan Θ = 2.4, therefore, Θ = tan¯¹2.4 = 67.38⁰

Now, to find the length of the ladder, we would have to apply SOHCAHTOA, that is, cos Θ = adjacent/hypotenuse = distance between the foot of the ladder and the wall / length of the ladder

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So, cos 67.38 = 50/ladder length

Therefore, ladder length = 50/cos 67.38 = 130cm

But observe that the answers were given in meters and not cm. converting, we have 130/100 = 1.3m

Now for the right answer to the above question:

  1. Option A is incorrect.
  2. Option B is incorrect.
  3. C is correct.
  4. D is not the correct answer.

KEY-POINTS…

You may please note these/this:

  • Use SOHCAHTOA for problems involving only right-angled triangle.
  • It is appropriate to firstly and quickly sketch problems like this to avoid mistakes.
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/ culled from 2020 JAMB-UTME mathematics past question 16 /

1 Answers

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