Embibe Experts Solutions for Chapter: Properties of Triangle, Exercise 1: EXERCISE-1

A vertical tower stands on a declivity which is inclined at $15°$ to the horizon. From the foot of the tower a man ascends the declivity for $80$ feet and then finds that tower subtends an angle of $30°$. The height of the tower is-

$A$ and $B$ are two points $30 \mathrm{m}$ apart in a line on the horizontal plane through the foot of a tower lying on opposite sides of the tower. If the distance of the top of the tower from $A$ and $B$ are $20 \mathrm{m}$ and $15 \mathrm{m}$ respectively, the angle of elevation of the top of the tower at $A$ is-

If $p_1, p_2, p_3$ are the altitudes of a triangle from its vertices $A, B, C$ and $∆$, the area of the triangle $ABC$, then $\frac{1}{p_1}+\frac{1}{p_2}-\frac{1}{p_3}$ is equal to -

If $a, b \text{and} A$ are given in a triangle and $c_1$ and $c_2$ are two possible values of third side such that $c_1^2+c_1{c}_2+c_2^2=a^2$, then $A$ is equal to-

In a triangle $\angle A=55°$ and $\angle B=15°$, then $\frac{c^2-a^2}{ab}$ is equal to

In a triangle $ABC, a:b:c=\sqrt{3}:1:1,$ then the triangle is

The sides of a triangle $ABC$ are $x,y, \sqrt{x^2+y^2+xy}$  respectively. The size of the greatest angle in radians is - 

In a $△ABC, \left(\frac{a^2}{\sin A}+\frac{b^2}{\sin B}+\frac{c^2}{\sin C}\right)·\sin \frac{A}{2}\sin \frac{B}{2}\sin \frac{C}{2}$ simplifies to -