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1

### 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 $$B$$.

$$40\sqrt 3 \,\,\,m,\,\,\,{60^ \circ },\,\,\,{45^ \circ }$$
2

### IIT-JEE 1989

Subjective
$$ABC$$ is a triangular park with $$AB=AC=100$$ $$m$$. A television tower stands at the midpoint of $$BC$$. The angles of elevetion of the top of the tower at $$A, B, C$$ are 45$$^ \circ$$, 60$$^ \circ$$, 60$$^ \circ$$, respectively. Find the height of the tower.

$$50\sqrt 3$$ $$m$$
3

### IIT-JEE 1988

Subjective
A sign -post in the form of an isosceles triangle $$ABC$$ is mounted on a pole of height $$h$$ fixed to the ground. The base $$BC$$ of the triangle is parallel to the ground. A man standing on the ground at a distance $$d$$ from the sign-post finds that the top vertex $$A$$ of the triangle subtends an angle $$\beta$$ and either of the other two vertices subtends the same angle $$\alpha$$ at his feet. Find the area of the triangle.

$$\left( {d\tan \beta - h} \right)\sqrt {{h^2}{{\cot }^2}\alpha - {d^2}}$$
4

### IIT-JEE 1986

Subjective
If in a triangle $$ABC$$, $$\cos A\cos B + \sin A\sin B\sin C = 1,$$ Show that $$a:b:c = 1:1:\sqrt 2$$

Solve it.

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