Question

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

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Answer 1

The value of cos C, is determined as 0.52.

The value of sin C, is determined as 0.85.

The value of tan C, is determined as 1.63.

How to calculate the value of cos C, sin C and tan C?

The value of cos C, sin C and tan C is calculated by applying the following trigonometry ratio as follows;

sin C = opposite leg / hypothenuse side

sin C = AB / CB

sin C = (26.4 ) / 30.9

sin C = 0.85

cos C = adjacent leg / hypothenuse side

cos C = AC / CB

cos C = 16.2 / 30.9

cos C = 0.52

tan C = sin C / cos C

tan C = (AB / CB ) / (AC / CB)

tan C = (AB / CB ) x (CB / AC)

tan C = AB / AC

tan C = 26.4 / 16.2

tan C = 1.63

Answer 2

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

Explanation:

According to the trigonometric ratios in aright triangle :

`\sin x =\frac{\text{Side opposite to x}}{\text{Hypotenuse}}\\\\\cos x =\frac{\text{Side adjacent to x}}{\text{Hypotenuse}}\\\\\tan x=(\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=\frac{\text{Side opposite to T}}{\text{Hypotenuse}}\\\\=(26.4)/(30.9)\approx0.85\\\\\cos x =\frac{\text{Side adjacent to T}}{\text{Hypotenuse}}\\\\=(16.2)/(30.9)\approx0.52\\\\\tan T=(\sin T)/(\cos T)\\\\=(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`