Question

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

Answer 1

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)

From (i) and (ii), we have

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