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1

### 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.

$$50\sqrt 3$$ $$m$$
2

### 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.

$$\left( {d\tan \beta - h} \right)\sqrt {{h^2}{{\cot }^2}\alpha - {d^2}}$$
3

### 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.
4

### IIT-JEE 1985

Subjective
In a triangle $$ABC$$, the median to the side $$BC$$ is of length $${1 \over {\sqrt {11 - 6\sqrt 3 } }}$$\$ and it divides the angle $$A$$ into angles $${30^ \circ }$$ and $${45^ \circ }$$. Find the length of the side $$BC$$.

$$2$$ units.

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