The distance between the points a cos 25- 0 and 0- a cos65- is -

Required distance =√((a cos25^∘ 0)^2+(0 a cos 65^∘)^2) =√(a^2cos^225^∘+a^2cos^265^∘) =√(a^2cos^225^∘+a^2cos^2(90^∘ 25^∘)) =√(a^2cos^225^∘+a^2sin^225^∘) = ...

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Byju's Answer

Standard X

Mathematics

Distance Formula

The distance ...

Question

The distance between the points $(a c o s 25^{\circ}, 0)$ and $(0, a c o s 65^{\circ})$ is ___.

$a c o s 35^{\circ}$

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$2 \sqrt{a}$

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$a$

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$0.5 a$

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Solution

The correct option is C
$a$

Required distance
$= \sqrt{(a c o s 25^{\circ} - 0)^{2} + (0 - a c o s 65^{\circ})^{2}} = \sqrt{a^{2} c o s^{2} 25^{\circ} + a^{2} c o s^{2} 65^{\circ}} = \sqrt{a^{2} c o s^{2} 25^{\circ} + a^{2} c o s^{2} (90^{\circ} - 25^{\circ})} = \sqrt{a^{2} c o s^{2} 25^{\circ} + a^{2} s i n^{2} 25^{\circ}} = \sqrt{a^{2} (c o s^{2} 25^{\circ} + s i n^{2} 25^{\circ})} = \sqrt{a^{2} \times (1)} = a$

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Similar questions

Q. Question 3 (ii)
Evaluate:
(ii)

s i n 25^{\circ} c o s 65^{\circ} + c o s 25^{\circ} s i n 65^{\circ}

Evaluate

$(i) \frac{{sin}^{2} 63^{\circ} + {sin}^{2} 27^{\circ}}{{cos}^{2} 17^{\circ} + {cos}^{2} 73^{\circ}}$

$(i i) sin 25^{\circ} cos 65^{\circ} + cos 25^{\circ} sin 65^{\circ}$

Q. What is the distance between the points A (c, 0) and B (0, −c)?

The distance between the points $(a c o s 25^{\circ}, 0)$ and $(0, a c o s 65^{\circ})$ is ___.

Q. The distance between the points

(a c o s 25^{\circ}, 0)

and

(0, a c o s 65^{\circ})

is ___.

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The distance between the points (a cos25∘,0) and (0,a cos65∘) is ___.

The correct option is C a Required distance =√(a cos25∘−0)2+(0−a cos 65∘)2=√a2cos225∘+a2cos265∘=√a2cos225∘+a2cos2(90∘−25∘)=√a2cos225∘+a2sin225∘=√a2(cos225∘+sin225∘)=√a2×(1)=a

The distance between the points $(a c o s 25^{\circ}, 0)$ and $(0, a c o s 65^{\circ})$ is ___.