C

|\
| \
| \
| \ A
| -----\
| |
| |1.7m
| |
| |
------- B
D

AB = 1.7m
CD:AB = 1.5 : 1

The angle of elevation of C from A is 52 degrees.

What is the length of BD.

Answer to 3 significant figures please.

Thanks

Answer in metres.

AB = 2x = 1.7

CD = 3x = 2.55
BD/CD = tan52°
BD = 2.55 tan52° = 3.264

To find the length of BD, we can use trigonometry and the given information.

First, let's find the length of CD. Since CD:AB = 1.5:1 and AB = 1.7m, we can calculate CD as follows:

CD = (1.5/1) * AB
CD = 1.5 * 1.7m
CD = 2.55m

Now, we can focus on triangle BCD. We know the length of CD (2.55m) and the angle of elevation of C from A (52 degrees). Let's label the angle at D as θ.

Using trigonometry, we can use the tangent function to find the length of BD:

tan θ = opposite/adjacent
tan θ = BD/CD

Rearranging the equation, we get:

BD = tan θ * CD

Substituting the values we have:

BD = tan 52° * 2.55m

Using a calculator, the approximate value of tan 52° is 1.2799. Therefore:

BD ≈ 1.2799 * 2.55m
BD ≈ 3.27m

So, the length of BD is approximately 3.27 meters (to 3 significant figures).

Note: It's always a good practice to check if the values make sense in the context of the diagram, so make sure that BD doesn't exceed the length of AB.