Archimedes went to sleep beside a big rock. he wanted to get up at 8 am, but the alarm clock was yet to be
invented! he decided to sleep at the spot where the rock's shadow should end when it's 8 am so as to be
awakened by the direct sunlight.
archimedes knew that at 8 am, the sunlight reaches the ground at an angle of 43°. the rock beside which he
slept was 7 meters tall.
how far from the rock did archimedes go to sleep?
round your final answer to the nearest hundredth.

Archimedes went to sleep 7.51 meters from the rock.

Step-by-step explanation:

We are told that the sunlight reaches the ground at an angle of 43°,  and that the rock is 7 meters tall.

The distance from the rock where Archimedes should sleep is:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.