Learn UNIT V: Trigonometry with Free Lessons & Tips

To find the height of the tower, we can use trigonometry.

Let's denote the height of the flagstaff as h meters.

Let's denote the height of the tower as h meters.

To prove the given expression for the height of the cloud above the lake, let's consider the scenario described.

Given:

1. The angles of depression from the top and bottom of the 8 m tall building are 30° and 45°, respectively.

We can form two right triangles to represent the situation.

For the top of the 8 m tall building: tan⁡(30∘)=8dtan(30∘)=d8

For the bottom of the 8 m tall building: tan⁡(45∘)=8dtan(45∘)=d8

We can solve these two equations simultaneously to find the values of hh and dd.

First, let's solve for dd using either equation (they are the same):

tan⁡(30∘)=8dtan(30∘)=d8

13=8d3

1=d8

d=83d=83

Now, using the value of dd, we can find the height of the multi-storeyed building using either equation:

tan⁡(30∘)=hdtan(30∘)=dh

13=h833

1=83

h

h=8h=8

So, the height of the multi-storeyed building is 8 meters, and the distance between the two buildings is 8383

Given:

We need to find all other values of trigonometric ratios based on this information.

To find the value of

Given: : : : : :

To prove:

Let's start by simplifying each term separately:

To prove:

Let's start with the left-hand side (LHS) of the equation: