Question

Ms. Lund placed a 7-foot ladder against a wall

with the base of the ladder 4 feet (ft.) away from
the wall. She decided that a different, 10-foot
ladder needed to be used. If Ms. Lund wants the
longer ladder to rest against the wall at the same
angle as the shorter ladder, about how far away
from the wall should she place its base?
A.
5.7 ft.
B.
6.0 ft.
C.
7.0 ft.
D.
8.1 ft.
E. 17.5 ft.

Answer 1

the answer is A, 5.7ft

step by step:

use trig, 7 is hypotenuse, 4 is opposite, theta(angle) is against wall. you have opp and hyp, sOH cah toa, so use sin. sinø=opp/hyp=4/7

therefore ø= sin^-1(4/7)= 34.85°

onto the next triangle with the ten foot ladder. since she wants it at the same angle from the wall,use 34.85°. you have the hypotenuse, the ladder, 10ft. so you once again use sin.

sin(34.84°) = opp/hyp

rearrange for opposite, the length from the house to the base of the ladder.

opp= sin(34.85°)(10)

opp=5.733ft, then round to 5.7ft.

Answer 2

We can solve this problem using the properties of similar triangles. When the shorter ladder is leaning against the wall, it forms a right triangle with the wall and the ground. The longer ladder will also form a similar right triangle with the wall and the ground when it is leaning against the wall at the same angle.

Let's call the distance that Ms. Lund needs to place the base of the longer ladder x feet away from the wall. Then, we can set up the following proportion between the two triangles:

7/4 = 10/x

We can cross-multiply to get:

7x = 40

And solve for x:

x = 40/7 ~ 5.7 ft

The answer is (A) 5.7ft