Applications of Trigonometry

The angle of elevation of a boat from a $15 \mathrm{m}$ high bridge is $30°$. If boat is moving with the speed of $6 \mathrm{km}/\mathrm{hr},$ then time taken by the boat to get under the bridge is

The horizontal distance between two towers is $60 m$. The angular elevation of the top of the taller tower as seen from the top of the shorter one is $30°$. If the height of the taller tower is $150 m$, the height of the shorter one approximately equal to_____.

An Airplane when flying at a height of $5000\mathrm{m}$ from the ground passes vertically above another Airplane at an instant, when the angles of elevation of the two Airplanes from the same point on the ground are$60º$ and $45º$Respectively. The vertical distance between the Airplanes at that instant is equal to______?

A satellite flying at height $h$ is watching the top of the two tallest mountains in Uttarakhand and Karnataka, them being Nanda Devi (height $7,816 \mathrm{m}$) and Mullayanagiri (height $1,930 \mathrm{m}$). The angles of depression from the satellite to the top of Nanda Devi and Mullayanagiri are $30°$ and $60°$ respectively. The distance between the peaks of the two mountains is $1937 \mathrm{km}$. The satellite is vertically above the midpoint of the distance between the two mountains. Find the distance between the peaks and the satellite.

If a shadow of a tower standing on a level ground is found to be $60 \mathrm{m}$ longer when sun's elevation is $30°$ than when it is $45°$, then the height of the tower is 

If the shadow of a tower standing on a level ground is found to be $60 \mathrm{m}$ longer when sun's elevation is $30°$ than when it is $45°$, then the height of the tower is

From a point E on the horizontal due east of a tree, the top of the trees makes an angle of elevation $60°$. From a point S on the horizontal due west of the tree the same top makes an angle of elevation $30°$. The angle of elevation made by the top of the tree at the mid point of ES is  

A pole is slightly inclined towards the east at an agle $\theta$. At two points due west of it at distances $a$ and $b$, the angles of elevation of the top of the pole are $\alpha$ and $\beta$ respectively. The inclination of the pole to the horizontal is

From a star, the angle of depression of two stars on the opposite side of the earth are $60°$ and $45°$. If the distance of the star from the earth is $1.98\times {10}^9 \mathrm{km}$, find the distance between the satellites.

From a star, the angle of depression of two satellites on the opposite side of the earth are $30°$ and $45°$. If the distance of the star from the earth is $2.5\times {10}^{11} \mathrm{km}$, find the distance between the satellites.

Find the height of the electric pole from the given data.

The top of a $15$ metre tower makes an angle of elevation of $60°$ with the bottom of an electronic pole and angle of elevation of $30°$ with the top of the pole.

Find the distance between the two boats if the wo boats are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are $30°$ and $45°$respectively and the lighthouse is $100 \mathrm{m}$ high.

The angle of elevation of a plane from a point on the ground is $60°$. After $15$ seconds flight, the elevation changes to $30°$. If the plane is flying at a height of $1500\sqrt{3} \mathrm{m}$ then speed of the plane is

The angle of elevation of the top of a $H \mathrm{m}$. high tower from two points $A$ and $B$ on the horizontal plane are $60° \text{and} 30°$ respectively. If the distance of $A$ from the foot of the tower is $a \mathrm{m}$. then the distance of $B$ from the foot of the tower will be _____$\mathrm{m}$.

A tree breaks into two parts due to heavy wind such that the upper part makes an angle of  $30°$with plane. The place where the upper part of the tree touches the ground is at a distance of $10\mathrm{m}$ from the base point of the tree. The height of the tree is

A circus artist is climbing on a $20 meter$ long rope which is tightly stretched and tied to the top of a vertical pole. If the angle made by the rope with the ground level is $30°$, then the height of the pole will be _____.

A plane flying at the height of $3000$m above the ground passes vertically above the another plane at an instant when the angle of elevation of the $2$ planes from the same point on the ground are $60°$ and $45°$ respectively. Then the height of the lower plane from the ground is

Angle of elevation of a tower from a point at a distance of $15$ centimeter from foot of the tower is $60°$. Then height of tower is

The string of a kite of length $100 \mathrm{m}$ makes an angle of $60°$ with the horizontal ground. Imaging that there is no slack in the string, the height of the kite from the ground is

The tip of a partially broken tree touches the ground at a point $10 \mathrm{m}$ from foot of it and makes an angle of elevation of $30°$ from the ground. Then, the height of the tree is