A 3m ladder stands on horizontal ground and reaches 2.8 m up a vertical wall. How far is the foot of the ladder from the base of the wall?

Step-by-step explanation:

let T be the top of the ladder

let F be the foot of the ladder

let B be the base of the wall

you need to find the distance between the foot of the ladder and the base of the wall, in other words the distance of the 'ground' ( refer to the diagram).

you are given that the hypotenuse - H is 3 m and that the opposite - O ( wall ) is 2.8 m.

i) find the angle

given

H, O → use SOH, sin.

sin x = opp. /hyp.

sin x = 2.8 / 3

x = sin-1 ( 2.8/ 3)

x = 68.960...

x = 70.0 ° ( 3 s.f)

ii) use either tan or cos to find the adjacent (wall)

using TOA, tan:

tan ( 68.96) = 2.8/ adj.

2.8 / adj. = tan (68.96)

adj. × tan (68.96) = 2.8

adj = 2.8/ tan (68.96)

adj = 1.0770...

adj. = 1.08 ( 3 sf)

base = 1.08 m

or you could rather simply work this out using Pythagoras Theorem:

where hyp. is c², the base is b² and height is a²;

c² = a² + b²

b² = c² - a²

b² = (3)² - (2.8)²

b² = 1.16

b = √1.16

b = 1.0770

b = 1. 08 m ( 3sf)

you can give your answer to 3 sf or 2 sf.

hope this helps you!

-s.

step-by-step explanation:

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