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

Answer:

z = 47.2°

w = 42.8°

y = 42.8°

x = 47.2°

Step-by-step explanation:

found altitude ('h') first:  6/h = h/7;  h = $\sqrt{42}$

found base by using Pythagorean Theorem:

7² + ($\sqrt{42}$)² = c²

c = $\sqrt{91}$

found angle z using Rule of Sines:

sin 90 / $\sqrt{91}$ = sin z / 7

arcsin z = 7 / $\sqrt{91}$ = 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