Manipur Board Solutions for Chapter: Trigonometry, Exercise 4: EXERCISE 10.4

A bridge over a river makes an angle of $45°$ with the river bank. If the length of the bridge over is 150m. The width of the river in metres is $k\sqrt{2}$. Find the value of $k$.

From a point on the ground $40 m$ away from the foot of a tower, the angle of elevation of the top of the tower is $30°$ and the angle of elevation of the top of a water tank is $45°$. Find the height of the tower.

From a point on the ground $40 m$ away from the foot of a tower, the angle of elevation of the top of the tower is $30°$ and the angle of elevation of the top of a water tank is $45°$. Find the depth of the tank.

A straight highway leads to the foot of a tower of height $50 m$. From the top of a tower, the angle of depression of two cars standing on the highway are $30° \& 60°$. What is the distance between the two cars, and how far is each car from the tower?

As observed from the top of a lighthouse $100 m$ above the water lever, the angles of depression of the two ships are $30° \& 45°$. If one ship is to the north and the other to the east of the lighthouse, find the between the two ships.

(Use $\sqrt{3}=1.732$)

The angles of elevation of the top of a tower from two points at distances $a \& b$ from the base and in the same straight line with it are complementary. Prove that height of the tower is $\sqrt{ab}$.

A tower subtends an angle $\alpha$ at a point on the same level as the foot of the tower and at a second point $h$ meters above the first, the depression of the foot of the tower is $\beta$. Show that the height of the tower is $h\tan \alpha cot\beta =b$.

A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height $h$. At a point on the plane, the angle of elevation of the bottom of the flagstaff is $\alpha$ and that of the top of the flagstaff is $\beta$. Prove that the height of the tower is $\frac{h\tan \alpha }{ \tan \beta -\tan \alpha }$