Given that sin (90-X)° = 0.8, where X is an acute angle, find without using mathematical tables the value of…

Question

Given that sin (90-X)° = 0.8, where X is an acute angle, find without using mathematical tables the value of tan X°.

ScanSolve AI Tutor · Accepted Answer

Haya Pretty, hapa kuna suluhisho la swali lako la trigonometry:

Swali: Ukipewa $\sin (90-X)^\circ = 0.8$ , ambapo $X$ ni pembe kali, pata thamani ya $\tan X^\circ$ bila kutumia jedwali za hisabati.

Tumia utambulisho wa trigonometric.
Tunajua kuwa $\sin (90^\circ - \theta) = \cos \theta$ .
Kwa hivyo, $\sin (90^\circ - X^\circ) = \cos X^\circ$ .
Kutokana na swali, $\sin (90^\circ - X^\circ) = 0.8$ .
Hii inamaanisha $\cos X^\circ = 0.8$ .
Badilisha thamani ya desimali kuwa sehemu na uwakilishe katika pembetatu mraba.
$\cos X^\circ = 0.8 = \frac{8}{10} = \frac{4}{5}$ .
Katika pembetatu mraba, $\cos X^\circ = \frac{\text{upande wa karibu}}{\text{hypotenuse}}$ .
Hivyo, upande wa karibu ni 4 na hypotenuse ni 5.
Tumia theorem ya Pythagoras kupata upande wa pili.
Wacha upande wa pili uwe $O$ .
$O^2 + (\text{upande wa karibu})^2 = (\text{hypotenuse})^2$ $O^2 + 4^2 = 5^2$ $O^2 + 16 = 25$ $O^2 = 25 - 16$ $O^2 = 9$ $O = \sqrt{9}$ $O = 3$
(Kwa sababu $X$ ni pembe kali, urefu wa upande lazima uwe chanya).
Pata thamani ya $\tan X^\circ$ .
$\tan X^\circ = \frac{\text{upande wa pili}}{\text{upande wa karibu}}$ $\tan X^\circ = \frac{3}{4}$
Thamani ya $\tan X^\circ$ ni $\boxed{\mathbf{\frac{3}{4}}}$ .

Given that sin (90-X)° = 0.8, where X is an acute angle, find without using mathematical tables the value of tan X°.