Question

The tops of two poles of heights 24 m and 20 m are connected by a wire. If the wire makes an angle
30° with the horizontal, what is the length of the wire.

Answer 1

Answer:

★ Length of wire = 8 m ★

Step-by-step explanation:

Given:

• Height of two poles are 24 m and 20 m
• Wire makes an angle of 30° with the horizontal

To Find:

• What is the length of wire ?

Solution: Let AB and CD be two poles where AB = 24 m and CD = 20 m

• A and C are joined by wire
• CE || DB and angle of elevation of A is 30°

• Let CE = DB = x •

→ Now AE = AB – EB = AB – CD = 24–20 = 4 m

★ In ∆ACE ,

$\small\implies{\sf }$ sinθ = Perpendicular/Hypotenuse = AE / AC

$\small\implies{\sf }$ sin30 = 4/AC

$\small\implies{\sf }$ 1/2 = 4/AC

$\small\implies{\sf }$ AC = 4 x 2

$\small\implies{\sf }$ AC = 8

∴ Length of AC( Wire) = 8 m