The sine ratio of an angle is the opposite side over the adjacent side.

Mathematics

1 answer:

Agata [3.3K]2 years ago

3 0

Answer:

never

Step-by-step explanation:

In a right triangle, every angle has an opposite side and an adjacent side. And there's always a hypotenuse.

The sine of an angle is the ratio of the length of the opposite side divided by the length of the hypotenuse.

The tangent ratio of an angle is the opposite side over adjacent side, it is not the sine ratio of a triangle.

For example, ABC is a right angled triangle having length of the sides are a,b,c.

$sine\ C=\frac{a}{c}$

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In the figure below, BCA ~ STR. Find cos C, sin C, and tan C. Round your answers to the nearest hundredth.

arsen [322]

Answer:

$\sin C\approx0.85\\\\\cos C \approx0.52\\\\\tan C\approx1.63$

Step-by-step explanation:

According to the trigonometric ratios in aright triangle :

$\sin x =\dfrac{\text{Side opposite to x}}{\text{Hypotenuse}}\\\\\cos x =\dfrac{\text{Side adjacent to x}}{\text{Hypotenuse}}\\\\\tan x=\dfrac{\sin x}{\cos x}$

Given: ΔBCA ~ ΔSTR

Since , corresponding angles of two similar triangles are equal.

So, ∠C = ∠T ...(i) [Middle letter]

In triangle STR

$\sin T=\dfrac{\text{Side opposite to T}}{\text{Hypotenuse}}\\\\=\dfrac{26.4}{30.9}\approx0.85\\\\\cos x =\dfrac{\text{Side adjacent to T}}{\text{Hypotenuse}}\\\\=\dfrac{16.2}{30.9}\approx0.52\\\\\tan T=\dfrac{\sin T}{\cos T}\\\\=\dfrac{0.85}{0.52}\approx1.63$ ...(ii)