10. tan (x + 15º) = 3 tan x
2007-02-08 15:53:01 · 3 answers · asked by homeschooled 1 in Science & Mathematics ➔ Mathematics
10. tan(x + 15º) = 3 tan x
tan(x + 15º) = (tanx + tan15°)/{1 - (tanx)(tan15°)} = 3tanx
tanx + tan15° = 3tanx - 3(tan²x)(tan15°)
0 = 2tanx - tan15° - 3(tan²x)(tan15°)
3(tan15°)(tan²x) - 2tanx + tan15° = 0
tanx = {2 ± √(4 - 12tan²15°)}/{6(tan15°)}
tanx = {2 ± √(4 - 12(2 - √3)²}/{6(2 - √3)}
tanx = {2 ± √(48√3 - 80}/{6(2 - √3)}
tanx = {2 ± 4√(3√3 - 5}/{6(2 - √3)}
tanx = {1 + 2√(3√3 - 5}/{3(2 - √3)} ≈ 2.3459447
The other solution is rejected.
x = 66.913024°, 246.913024°
Plug the answer into your calculator. You will see it works.
2007-02-08 16:27:44 · answer #1 · answered by Northstar 7 · 0⤊ 0⤋
Northstar seem pretty close.
His rejected answer seems okay, tho, to me.
The rejected tan x = approximately .1421 making the angle x = 8.0913 (or 188.0913). Either of these angles should check out too.
(I'm assuming that the 10 is the number of your problem; that it otherwise doesn't affect the problem. Otherwise we're all off.)
2007-02-09 00:47:59 · answer #2 · answered by answerING 6 · 0⤊ 0⤋
tan cancels, you have x+ 15 = 3x
15/2 is 7.5
2007-02-09 00:25:02 · answer #3 · answered by Grant G 5 · 0⤊ 1⤋