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PLEASE HELP :) LOTS OF POINTS + BRAINLY
Jackson loves an adventure but always wants to know what he is getting himself into before he jumps in completely. He decides to take a rock climbing course. He arrives at the course which is meeting at the base of the mountain. He looks up and decides he needs to know how far UP he will be climbing. The instructor doesn’t know the height of this location (Jackson is starting to doubt the instructor’s ability if he doesn't know this simple fact) Jackson needs to figure out a way to know the approximate height before climbing. Jackson decides to use his highschool geometry skills to determine the height. He needs a mirror and luckily another climber pulls one out of his backpack. Jackson places the mirror on the ground so that he is able to look at the mirror and see the top of the mountain.
The mirror is 5 feet in front of him and is approximately 40 feet from the base of the mountain. ∆ Jackson is 6’4” tall. Approximately how high is the top of the mountain.
Draw a sketch to illustrate the process and be sure to use mathematical language to show and explain your work.

Sagot :

Jackson's method to figure out the height of the mountain is from the

similar triangles formed by the light using the mirror.

Response:

  • The height of the mountain is 50 feet 8 inches

Which methods can used to find the height of the mountain?

The given parameters are;

Distance of the mirror from Jackson = 5 feet

Distance of the mirror from the base of the mountain = 40 feet

Height of Jackson = 6'4'' tall

Required:

The approximate height of the mountain, h

Solution:

The triangles formed by the light from the top of the mountain which is

reflected to Jackson from the mirror, Jackson's height, the height of the

mountain, and their distances from the mirror, are similar triangles.

The ratio of corresponding sides of similar triangles are equal, therefore,

we have;

[tex]\dfrac{Jackson's \ height}{Jackson's \ distance \ from \ the \ mirror } =\mathbf{ \dfrac{Height \ of \ the \ mountain}{Distance \ of \ the \ mountain \ from \ the \ mirror}}[/tex]

Which gives;

[tex]\dfrac{6\frac{1}{3} \, ft.}{5 \, ft.} = \mathbf{ \dfrac{h}{40 \, ft.}}[/tex]

[tex]h = 480 \, in. \times \dfrac{76 \, in.}{60 \, in.} = 608 \, in. = \mathbf{50 \frac{2}{3} \, ft. = 50 \, feet \ 8 \, inches}[/tex]

  • The height of the mountain is approximately 50 feet 8 inches

Learn more about similar triangles here:

https://brainly.com/question/23467926

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