Geometry

Trigonometry

Easy

Two men on either side of a pole of 30 m high observe its top at angles of elevation $\alpha$ and $\beta$ respectively. The distance between the two men is $40\sqrt{3}$ m and the distance between the first man at A and the pole is $30\sqrt{3}$ m.

Figure for CUET Mathematics 2022 10 Aug Shift 1 question 42 (Geometry)

Based on the above information, answer the question:

$\tan(\alpha + \beta) =$

$\sqrt{3} + \frac{1}{\sqrt{3}}$

$\sqrt{3} - \frac{1}{\sqrt{3}}$

$2\sqrt{3} - 1$

Infinite (does not exist)

✅ Correct Option: 4

$DC = 40\sqrt{3} - 30\sqrt{3} = 10\sqrt{3}$ . So $\tan\beta = \frac{30}{10\sqrt{3}} = \sqrt{3}$ , giving $\beta = \pi/3$ . Then $\alpha + \beta = \pi/6 + \pi/3 = \pi/2$ , and $\tan(\pi/2)$ is undefined (infinite).

Question 41

The value of $\alpha$ is

Question 43

Area of $\triangle ABD$ is

Question 44

$\angle ABC$ is equal to:

Question 45

The value of $\frac{1}{AB^2} + \frac{1}{BC^2}$ is:

tan⁡(α+β)=\tan(\alpha + \beta) =tan(α+β)=

Solution

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Keyboard Shortcuts

CUET Mathematics Past Year Questions (Topic-Wise)

$\tan(\alpha + \beta) =$