Video: CBSE Class X • Pack 2 • 2017 • Question 3

CBSE Class X • Pack 2 • 2017 • Question 3

02:27

Video Transcript

If a 30-meter high tower casts a 10 square root of three meter long shadow on the ground, what is the angle of elevation of the sun?

We have a tower and our tower casts a shadow. The tower is 30 meters tall and the shadow 10 square root of three meters long. This would be the angle of elevation made with the sun. What we should notice now is that we have an opposite side measure and an adjacent side measure to our angle. In addition to that, we will note that the tower makes a right angle with its shadow.

Having opposite and adjacent side lengths in a right triangle tells us that we’ll be looking for a tangent ratio. Tangent of our missing angle is equal to the opposite side measure, 30, over the adjacent side measure, 10 square root of three. We noticed that this angle can be simplified. 30 divided by 10 equals three. We can reduce this to three over the square root of three.

To simplify a bit further, we want to take the square root of three and try to get it out of the denominator. To do that, we multiply this fraction by the square root of three over the square root of three. The numerator of that is three times the square root of three. And in the denominator, we need to put the square root of three times the square root of three, which equals three.

And now, we have a fraction that has three over three. That three over three cancels out. And we’re left with the square root of three. The tangent of our missing angle is the square root of three. And this is a form we should recognize. We know that the tangent of 60 degrees equals the square root of three. And that means that our missing angle must measures 60 degrees. The angle of elevation of the sun, here, is 60 degrees.

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