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The angle of elevation of the top of a tower at a point on the ground 50 m away from the foot of the tower is 45°. Then the height of the tower (in metres) is

a) $$50\sqrt 3 $$
b) $$50$$
c) $$\frac{{50}}{{\sqrt 2 }}$$
d) $$\frac{{50}}{{\sqrt 3 }}$$

Answer: b
Explanation: Let AB be tower and C is a point on the ground 50 m away
q40
From foot of tower B
Angle of elevation is 45°
Let h be height of tower = x m
$$\eqalign{ & \tan \theta = \frac{{AB}}{{BC}} \cr & \tan {45^ \circ } = \frac{{AB}}{50} \cr & 1 = \frac{{AB}}{{50}} \Rightarrow AB = 50\,m \cr} $$

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