A surveyor wishes to measure the width of a trench. He places a transit telescope in a position on one side of the trench that is 18 feet higher than the second location. The surveyor reads the angle of depression from the transit telescope and finds that it is 31°, as shown in the diagram below. If the transit telescope is 4.5 feet above the ground at the first location during this reading, how wide is the trench?

Include all relevant calculations and use the correct units for all measures. Be sure explanations are written in complete sentences.

Bismuth-210 is an isotope that radioactively decays by about 13% each day, meaning 13% of the remaining bismuth-210 transforms into another atom (polonium-210 in this case) each day. if you begin with 233 mg of bismuth-210, how much remains after 8 days?

List the sides of δrst in in ascending order (shortest to longest) if: a ∠r =x+28°, m∠s = 2x+16°, and m∠t = x+12°

Christine wong has asked dave and mike to her move into a new apartment on sunday morning. she has asked them both, in case one of them does not show up. from past experience, christine knows that there is a 40% chance that dave will not show up and a 30% chance that mik a. what is the probability that both dave and mike will show up? (round your answer to 2 decimal places.) b. what is the probability that at least one of them will show up? c. what is the probability that neither dave nor mike will show up? (round your answer to 2 decimal places.)e will not show up. dave and mike do not know each other and their decisions can be assumed to be independent.