Question 51

# Two lighthouses, located at points A and B on the earth, are 60 feet and 40 feet tall respectively. Each lighthouse is perfectly vertical and the land connecting A and B is perfectly flat. The topmost point of the lighthouse at A is A’ and of the lighthouse at B is B’. Draw line segments A’B and B’A, and let them intersect at point C’. Drop a perpendicular from C’ to touch the earth at point C. What is the length of CC’ in feet?

Solution

Triangle ACC' is similar to triangle ABB'

Considering AC = a, BC = b, CC' = h, AA' is given as 60, BB' is given to be 40.

AC/AB = CC'/BB' = h/40.

$$\left(\frac{a}{a+b}\right)\ =\ \frac{h}{40}$$  (1)

Similarly triangle BCC' is similar to BAA'.

BC/AB = CC'/AA' = h/60.

$$\left(\frac{b}{a+b}\right)\ =\ \frac{h}{60}$$  (2)

Adding (1) and (2).

$$\frac{h}{40}+\frac{h}{60\ }=\ 1$$

1/h = $$\left(\frac{1}{40}+\frac{1}{60}\right)$$

h = 24

Using crossed ladder theorem

$$\frac{1}{CC'}=\frac{1}{AA'}+\frac{1}{BB'}$$=1/60 +1/40 =5/120 =24.

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## CAT Verbal Ability Questions | VARC Questions For CAT

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The passage contains a detailed mathematical question about the height of the intersection point of two line segments formed by the tops of two lighthouses and the ground. The solution to the problem is also provided, including the final answer.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
Question 51

# Two lighthouses, located at points A and B on the earth, are 60 feet and 40 feet tall respectively. Each lighthouse is perfectly vertical and the land connecting A and B is perfectly flat. The topmost point of the lighthouse at A is A’ and of the lighthouse at B is B’. Draw line segments A’B and B’A, and let them intersect at point C’. Drop a perpendicular from C’ to touch the earth at point C. What is the length of CC’ in feet?

Solution

Triangle ACC' is similar to triangle ABB'

Considering AC = a, BC = b, CC' = h, AA' is given as 60, BB' is given to be 40.

AC/AB = CC'/BB' = h/40.

$$\left(\frac{a}{a+b}\right)\ =\ \frac{h}{40}$$  (1)

Similarly triangle BCC' is similar to BAA'.

BC/AB = CC'/AA' = h/60.

$$\left(\frac{b}{a+b}\right)\ =\ \frac{h}{60}$$  (2)

Adding (1) and (2).

$$\frac{h}{40}+\frac{h}{60\ }=\ 1$$

1/h = $$\left(\frac{1}{40}+\frac{1}{60}\right)$$

h = 24

Using crossed ladder theorem

$$\frac{1}{CC'}=\frac{1}{AA'}+\frac{1}{BB'}$$=1/60 +1/40 =5/120 =24.

### Video Solution

Create a FREE account and get:

• All Quant Formulas and shortcuts PDF
• XAT previous papers with solutions PDF
• XAT Trial Classes for FREE

## CAT Verbal Ability Questions | VARC Questions For CAT

Boost your Prep!
user
The passage contains a detailed mathematical question about the height of the intersection point of two line segments formed by the tops of two lighthouses and the ground. The solution to the problem is also provided, including the final answer.

TYPE: SINGLE_QUESTION_WITH_ANSWER