Find $AD$
View full solution →Question types
Height and Distances question types
51 questions across 4 question groups — pick any mix to generate a Mathematics paper with step-by-step answer keys.
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Sample Questions
Height and Distances questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Find $AD$
View full solution →The height of a tree is $\sqrt3$ times the length of its shadow. Find the angle of elevation of the sun.
View full solution →Calculate $BC $.
View full solution →In the following diagram , $AB$ is a floor $-$ board : $\text{PQRS}$ is a cubical box with each edge $= 1m$ and $\angle B = 60^\circ $. Calculate the lenght of the board $AB.$
View full solution →The angle of elevation of the top of a tower is observed to be$ 60^\circ$ . At a point, $30 m$ vertically above the first point of observation, the elevation is found to be $45^\circ$ . Find:
$(i)$ the height of the tower,
$(ii)$ its horizontal distance from the points of observation.
View full solution →$(i)$ the height of the tower,
$(ii)$ its horizontal distance from the points of observation.
From the figure , given below , calculate the lenth of CD .
In the figure, given below, it is given that $AB$ is perpandiculer to $BD$ and is of length $X$ metres. $DC = 30m .\angle ADB = 30^\circ$ and $\angle ACB = 45^\circ . $Without using tables, find $X$
View full solution →The angles of elevation of the top of a tower from two points on the ground at distances $a$ and $b$ metres from the base of the tower and in the same line are complementary. Prove that the height of the tower is sqrtab metre.
View full solution →With reference to the given figure, a man stands on the ground at point $A,$ which is on the same horizontal plane as $B,$ the foot of the vertical pole $BC.$ The height of the pole is $10 m.$ The man's eyes $2 m$ above the ground. He observes the angle of elevation of $C,$ the top of the pole, as $x^o,$ where $\tan x^o$ $=\frac{2}{5}$.
Calculate :
$(i)$ the distance $AB$ in metres.
$(ii)$ angle of elevation of the top of the pole when he is standing $15$ metres from the pole. Give your answer to the nearest degree.
View full solution →Calculate :
$(i)$ the distance $AB$ in metres.
$(ii)$ angle of elevation of the top of the pole when he is standing $15$ metres from the pole. Give your answer to the nearest degree.
A vertical tower stand on a horizontel plane and is surmounted by a vertical flagstaff of height h metre. At a point on the plane, the angle of elevation of the bottom of the flagstaff is $∝$ and at the top of the flagstaff is $\beta$ . prove that the height of the tower is
$\frac{ h \tan \alpha}{\tan \beta-\tan \alpha}$
View full solution →$\frac{ h \tan \alpha}{\tan \beta-\tan \alpha}$
At a point on level ground, the angle of elevation of a vertical tower is found to be such that its tangent is $5/12$. On walking $192$ metres towards the tower, the tangent of the angle is found to be $3/4$. Find the height of the tower.
View full solution →The angles of depression of two ships $A$ and $B$ as observed from the top of a lighthouse $60\ m$ high are $60^\circ$ and $45^\circ$ respectively. If the two ships are on the opposite sides of the lighthouse, find the distance between the two ships, Give your answer correct to the nearest whole number.
View full solution →The radius of a circle is given as $15 \ cm$ and chord $AB$ subtends an angle of $131^\circ$ at the centre $C$ of the circle. Using trigonometry, calculate:
$(i)$ the length of $AB$;
$(ii)$ the distance of $AB$ from the centre $C$.
View full solution →$(i)$ the length of $AB$;
$(ii)$ the distance of $AB$ from the centre $C$.
A vertical tower is $20\ m$ high. A man standing at some distance from the tower knows that the cosine of the angle of elevation of the top of the tower is $0.53$. How far is he standing from the foot of the tower?
View full solution →From a window $A , 10\ m $ above the ground the angle of elevation of the top $C$ of a tower is $X ^\circ ,$ Where $ \tan x^{\circ}=\frac{5}{2}$ and the angle of depression of the foot $D$ of the tower is $Y^\circ ,$ Where $\tan y^{\circ}=\frac{1}{4}$.calculate the height $CD$ of the tower in metres .
View full solution →The horizontal distance between two towers is 75 m and the angular depression of the top of the first tower as seen from the top of the second, which is 160 m high, is 45°. Find the height of the first tower.
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