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1

### IIT-JEE 1991

Subjective
In a triangle of base a the ratio of the other two sides is $$r\left( { < 1} \right)$$. Show that the altitude of the triangle is less than of equal to $${{ar} \over {1 - {r^2}}}$$

Solve it.
2

### IIT-JEE 1991

Subjective
A man notices two objects in a straight line due west. After walking a distance $$c$$ due north he observes that the objects subtend an angle $$\alpha$$ at his eye; and, after walking a further distance $$2c$$ due north, an angle $$\beta$$. Show that the distance between the objects is $${{8c} \over {3\cot \beta - \cot \alpha }}$$; the height of the man is being ignored.

Solve it.
3

### IIT-JEE 1991

Subjective
The sides of a triangle are three consecutive natural numbers and its largest angle is twice the smallest one. Determine the sides of the triangle.

$$4, 5, 6$$
4

### IIT-JEE 1990

Subjective
A vertical tower $$PQ$$ stands at a point $$P$$. Points $$A$$ and $$B$$ are located to the South and East of $$P$$ respectively. $$M$$ is the mid point of $$AB$$. $$PAM$$ is an equilateral triangle; and $$N$$ is the foot of the perpendicular from $$P$$ and $$AB$$. Let $$AN$$$$=20$$ mrtres and the angle of elevation of the top of the tower at $$N$$ is $${\tan ^{ - 1}}\left( 2 \right)$$. Determine the height of the tower and the angles of elevation of the top of the tower at $$A$$ and $$B$$.

$$40\sqrt 3 \,\,\,m,\,\,\,{60^ \circ },\,\,\,{45^ \circ }$$

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