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Trigonometric Functions

Short Answer Type

21. The angles of a triangle are in A.P. and the number of degrees in the least angle is to the number of radians in the greatest angle is 60 :

straight pi

. Find the angles in degrees.

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22. Assuming the average distance of the earth from the sun to be 149,700,000 km, and the angle subtended by the sun at the eye of a person on the earth to be 32’, find the sun’s diameter.

Let D km denote the diameter of the sun. Since the angle subtended by the sun is very small, therefore, its diameter is approximately equal to small arc of a circle with centre at the eye of the observer on the earth.

∴ l = D, r = 149,700,000 km

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Since $straight theta space equals space l over r rightwards double arrow space fraction numerator 2 straight pi over denominator 15 space cross times space 45 end fraction space equals space fraction numerator straight D over denominator 149 comma space 700 comma space 000 end fraction$

$rightwards double arrow$ $straight D space equals space 2 over 675 space cross times space 22 over 7 space cross times space 149 comma 700 comma 000 space left parenthesis Approx. right parenthesis space equals space 1 comma 394 comma 000 space km space left parenthesis Approx right parenthesis.$