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1

### 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.

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

### 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.
3

### 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.
4

### IIT-JEE 1985

Subjective
A ladder rests against a wall at an angle $$\alpha$$ to the horizintal. Its foot is pulled away from the wall through a distance $$a$$, so that it slides $$a$$ distance $$b$$ down the wall making an angle $$\beta$$ with the horizontal. Show that $$a = b\tan {1 \over 2}\left( {\alpha + \beta } \right)$$

Solve it.

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