Question

The sun subtend an angle at 35degree from the centre of the earth whose distant from the centre of the earth is 382,100km. Find the diameter of the sun

Answer 1

Study the figure attached below:

Answer:

240951.33km      

Step-by-step explanation:

For this type of question first we need to draw the figure as shown in the attached file (Figure.1).

Looking at the figure, we can see that triangle ABC is formed by bisecting the angle 35 degree (i.e. if the angle is bisected, it will divide into two equal parts, so 35 degree will divide into two equal parts of 17.5 degree).

As the triangle ABC is a right triangle, so we can use the trigonometric ratios to find the diameter of the sun.

$tan(\theta )= \frac{perpendicular}{Base}$

In the triangle ABC, perpendicular (opposite side to $\theta$ ) is BC and base (Adjacent side) is AC

$tan(\theta)=\frac{BC}{AC}$

$\theta$=17.5 degree

AC=382100km

Putting the values, we get

$tan(17.5)=\frac{BC}{382100}\\ \\BC=tan(17.5)*382100km\\\\BC=0.315*382100km\\\\BC=120475.66km$

Diameter=d=2*Radius

As BC is the distance from center of the sun, it is the radius, so we can find the diameter if we multiply it by 2.

Diameter of the sun=d=2*120475.66km

$The\ diameter\ of\ the\ sun\ = 240951.33km$