Question

Find the value of each variable. Round to the nearest tenth. How does the measure of angle x compare to the measure of angle z? Justify.

Answer 1

z = 47.2°

w = 42.8°

y = 42.8°

x = 47.2°

Explanation:

found altitude ('h') first: 6/h = h/7; h =
`√(42)`

found base by using Pythagorean Theorem:

7² + (
`√(42)`)² = c²

c =
`√(91)`

found angle z using Rule of Sines:

sin 90 /
`√(91)` = sin z / 7

arcsin z = 7 /
`√(91)` = 47.2°

found angle w by adding 90 and 47.2, then subtracting from 180 to get 42.8°

found angle y by subtracting m∡z from 90° to get 42.8°

found angle x by adding 90 and 42.8°, then subtracting from 180